There seems to be a bit of a discussion about Battle Chateau vs Le Wow as far as the "Best Exp Grinding Spot" in the game. Since it takes so long for the Battle Chateau to reach "Grand Duke" or "Grand Dutchess" level, I think people may be concerned with exactly what Battle Chateau offers over Le Wow.
Introduction
The Battle Chateau is a building on Route 7, accessible pretty early in the game. You start off at rank "Baron", and fight level 15 opponents. The ranks are as follows:
Baron/Baroness (Initial)
Viscount/Viscountess (Defeat 5 opponents)
Earl/Countess (Defeat 20 Trainers)
Marquis/Marchioness Defeat (40 Trainers)
Duke/Duchess (Defeat 140 Trainers)
Grand Duke/Duchess (Defeat all Trainers at Battle Chateau)
At Marquis / Marchioness level, the Gym Leaders begin to visit the Battle Chateau. At Duke / Duchess level, the Elite 4 begin to visit. Finally, at Grand Duke / Duchess level, the Grand Duchess / Champion Diantha begins to visit.
Once you reach these higher levels, the Battle Chateau becomes one of the best leveling spots and money grinding spots in the game.
Writs
Writs are expensive bonuses you pay for that greatly effects the Battle Chateau payout, levels of your opponent, and how often opponents visit the Battle Chateau. These writs stay in effect until the next midnight. Writs cost anywhere from $50,000 to $300,000... with the more useful writs costing more money. As you level up in rank, you gain the ability to write more useful writs, such as the Silver Writ, the Gold Writ, and finally the Black Writ.
Writs can stack with each other, although writs of the same type cancel each other out. For example, the Black Writ (+20 Levels to all opponent's Pokemon) cannot be combined with the Red Writ (+10 Levels to all opponent's Pokemon). You can however stack the Silver, Gold, and Black Writ at the same time.
My recommendations? Use the Silver Writ if you plan on doing more than 5 battles at the Chateau, the speed at which the new trainers comes in is easily worth the $100,000 cost. The Gold Writ multiplies your money by 150%. The $100,000 cost is also steep, but you will easily make it up with the Gold Writ.
Finally, the Black Writ increases the level of your opponent's `mon by 20 levels. It also increases the money gain by some amount (it is different for each trainer). However, because the cost of the Only use the Black Writ when you are willing to spend tons of money on leveling up your pokemon. +20 levels to all trainers greatly increases your exp gain, especially when you find Duchess Rosile (who will have three level 65 Audinos when the Black Writ is active).
Opponents
Maids, Butlers, Rich Boys, and Ladies don't seem special. They occasionally are at the Duke / Duchess level and offer good experience, but they don't make nearly as much money or experience as the richer opponents. Nonetheless, you may get a bad run of opponents, and when that happens, you might as well fight these opponents at random and hope for the best.
Now the Madame and Monsieurs are extremely rich. The lowest-ranked barons give $21,000 per battle (with Amulet Coin+Gold Writ). Not bad at all for taking out a single lvl 15 Burmy (35 with Black Writ).
On the high end, I've noticed that certain named Dukes (ie: Duke Hennessy) give over $50,000 per battle with Amulet Coin+Gold Writ.
If you get lucky and encounter Duke Hennessy with O-Power lvl 3 active, you will get over $150,000 in a single battle. Remember, O-Power Lvl3 stacks with everything else. Realistically speaking, you can expect to make a profit of $200,000 to $300,000 in the three minutes that O-Power lvl3 is active... so long as you focus on these rich old people for their money.
Furisode Girl (Aka: Tons of Audinos)
Furisode Girls ALWAYS have Audinos, making them the highest experience opponents in the game. With the Black Writ active, "Marchioness" rank Furisode girls have two lvl 60 Audinos, while "Duchess" rank Fuisode girls have three lvl 65 Audinos.
If you ever see two or more Furisode Girls together, activate Experience Power Lvl3 for easy 50,000+ experience... or even more if you have the Lucky Egg.
Gym Leaders:
Base Prize: $8000
Black Writ Prize: $11300
With Amulet Coin + Gold Writ + Black Writ: $33900
With Amulet Coin + Gold Writ + Lvl 3 O-Power: $100,800
Gym Leaders aren't quite as rich as the Duke and Duchess level Madames or Monsieurs. However, they give excellent amounts of experience and are guaranteed to be lvl 50 opponents. With the Black Writ active, they rocket up to lvl 70.
A single Gym Leader + Amulet Coin + Lvl 3 O-Power guarantees that you will gain a profit from a Gold Writ. Multiple Gym Leaders give you a huge opportunity to make tons and tons of money, with a properly timed Lvl 3 O-Power. Or, if you are focused on Experience, the +Experience O-Power is useful on Gym leaders.
Every Gym Leader rematch has two pokemon that they draw from.
Elite 4
Base Prize: $11000
Black Writ Prize: $15000
With Amulet Coin + Gold Writ + Black Writ: $45000
With Amulet Coin + Gold Writ + Black Writ + Lvl 3 O-Power: $135000
The Elite4 Members are just like the Gym Leaders, except with more money, more experience, and more powerful pokemon. These Dukes and Duchesses have three pokemon each at level 55 (Level 75 with Black Writ)
Champion
Base Prize: $14400
Black Writ: $19200
With Amulet Coin + Gold Writ: $57600
With Amulet Coin + Gold Writ + Lvl 3 O-Power: $172800
Champion Diantha stomps into the Battle Chateau with FOUR level 60 pokemon (level 80 with Black Writ). With so much experience and money gained from facing the champion, its basically worth it to spend all of your O-Powers and activating all the Writs for this battle.
Le Wow vs Battle Chateau
The Battle Chateau is far better for money than Le Wow. With only $200,000 investment for the Silver and Gold Writs and Amulet Coin, it becomes possible to earn $21,000+ per battle if you solely focus on the "old men" and "old women". With O-Power lvl3 stacked, you'll be earning anywhere from $63,000 to $150,000 per battle with proper opponent selection.
For experience, the Battle Chateau seems to have the edge as long as you can afford the $400,000 Black Writ and Silver Writ. However, the experience gained here is somewhat random. If you only have Rich Boys and Ladies to face, you don't really know if you're gonna be fighting a lvl 35 Ralts, or a lvl 60 Haxorus. Nevertheless, with proper "opponent selection", you can focus on Elite 4 (lvl 75), Gym Leaders (lvl 70), and Furisode Girls (lvl 60 and 65 Audinos) and gain a significant amount of experience points.
In the worst case, you may spend a few battles facing lvl 35 Burmys or Ralts, but within 5 minutes, the Silver Writ will flush out all of the trainers and give you a fresh new start.
Le Wow Triple-Battles / Rotation Battles on the other hand consistently offers lvl 63 Pokemon, and your O-Power for +Experience will last for all 5 trainers / 15 Pokemon. However, since you pay $90,000 to enter the restaurant, and only get ~$125,000 in profits after selling the Balm Mushrooms (with lvl 3 exp O-Power / Lvl 1 +money O-Power), I know for a fact that the Battle Chateau offers far more money than Le Wow offers you.
Finally, Le Wow Rotation Battles have a slow and annoying "level up" bar. Leveling a Pokemon from lvl 1 to lvl 15 takes but a single battle in Le Wow... but the amount of time lost waiting for the level bar to fill up is painful. While Le Wow Rotation battles offer significant amounts of experience points... my personal experience has me shying away from them, especially when raising baby-level Pokemon to higher levels.
After all, once you pay the $200,000 for the Silver and Gold writ, the Battle Chateau doesn't require any more investment until midnight. You have to pay $90,000 per Le Wow visit.
Introduction
The Battle Chateau is a building on Route 7, accessible pretty early in the game. You start off at rank "Baron", and fight level 15 opponents. The ranks are as follows:
Baron/Baroness (Initial)
Viscount/Viscountess (Defeat 5 opponents)
Earl/Countess (Defeat 20 Trainers)
Marquis/Marchioness Defeat (40 Trainers)
Duke/Duchess (Defeat 140 Trainers)
Grand Duke/Duchess (Defeat all Trainers at Battle Chateau)
At Marquis / Marchioness level, the Gym Leaders begin to visit the Battle Chateau. At Duke / Duchess level, the Elite 4 begin to visit. Finally, at Grand Duke / Duchess level, the Grand Duchess / Champion Diantha begins to visit.
Once you reach these higher levels, the Battle Chateau becomes one of the best leveling spots and money grinding spots in the game.
Writs
Writs are expensive bonuses you pay for that greatly effects the Battle Chateau payout, levels of your opponent, and how often opponents visit the Battle Chateau. These writs stay in effect until the next midnight. Writs cost anywhere from $50,000 to $300,000... with the more useful writs costing more money. As you level up in rank, you gain the ability to write more useful writs, such as the Silver Writ, the Gold Writ, and finally the Black Writ.
Writs can stack with each other, although writs of the same type cancel each other out. For example, the Black Writ (+20 Levels to all opponent's Pokemon) cannot be combined with the Red Writ (+10 Levels to all opponent's Pokemon). You can however stack the Silver, Gold, and Black Writ at the same time.
My recommendations? Use the Silver Writ if you plan on doing more than 5 battles at the Chateau, the speed at which the new trainers comes in is easily worth the $100,000 cost. The Gold Writ multiplies your money by 150%. The $100,000 cost is also steep, but you will easily make it up with the Gold Writ.
Finally, the Black Writ increases the level of your opponent's `mon by 20 levels. It also increases the money gain by some amount (it is different for each trainer). However, because the cost of the Only use the Black Writ when you are willing to spend tons of money on leveling up your pokemon. +20 levels to all trainers greatly increases your exp gain, especially when you find Duchess Rosile (who will have three level 65 Audinos when the Black Writ is active).
Opponents

Maids, Butlers, Rich Boys, and Ladies don't seem special. They occasionally are at the Duke / Duchess level and offer good experience, but they don't make nearly as much money or experience as the richer opponents. Nonetheless, you may get a bad run of opponents, and when that happens, you might as well fight these opponents at random and hope for the best.

Now the Madame and Monsieurs are extremely rich. The lowest-ranked barons give $21,000 per battle (with Amulet Coin+Gold Writ). Not bad at all for taking out a single lvl 15 Burmy (35 with Black Writ).
On the high end, I've noticed that certain named Dukes (ie: Duke Hennessy) give over $50,000 per battle with Amulet Coin+Gold Writ.
If you get lucky and encounter Duke Hennessy with O-Power lvl 3 active, you will get over $150,000 in a single battle. Remember, O-Power Lvl3 stacks with everything else. Realistically speaking, you can expect to make a profit of $200,000 to $300,000 in the three minutes that O-Power lvl3 is active... so long as you focus on these rich old people for their money.
Furisode Girl (Aka: Tons of Audinos)

Furisode Girls ALWAYS have Audinos, making them the highest experience opponents in the game. With the Black Writ active, "Marchioness" rank Furisode girls have two lvl 60 Audinos, while "Duchess" rank Fuisode girls have three lvl 65 Audinos.
If you ever see two or more Furisode Girls together, activate Experience Power Lvl3 for easy 50,000+ experience... or even more if you have the Lucky Egg.
Gym Leaders:

Base Prize: $8000
Black Writ Prize: $11300
With Amulet Coin + Gold Writ + Black Writ: $33900
With Amulet Coin + Gold Writ + Lvl 3 O-Power: $100,800
Gym Leaders aren't quite as rich as the Duke and Duchess level Madames or Monsieurs. However, they give excellent amounts of experience and are guaranteed to be lvl 50 opponents. With the Black Writ active, they rocket up to lvl 70.
A single Gym Leader + Amulet Coin + Lvl 3 O-Power guarantees that you will gain a profit from a Gold Writ. Multiple Gym Leaders give you a huge opportunity to make tons and tons of money, with a properly timed Lvl 3 O-Power. Or, if you are focused on Experience, the +Experience O-Power is useful on Gym leaders.
Every Gym Leader rematch has two pokemon that they draw from.
Elite 4

Base Prize: $11000
Black Writ Prize: $15000
With Amulet Coin + Gold Writ + Black Writ: $45000
With Amulet Coin + Gold Writ + Black Writ + Lvl 3 O-Power: $135000
The Elite4 Members are just like the Gym Leaders, except with more money, more experience, and more powerful pokemon. These Dukes and Duchesses have three pokemon each at level 55 (Level 75 with Black Writ)
Champion

Base Prize: $14400
Black Writ: $19200
With Amulet Coin + Gold Writ: $57600
With Amulet Coin + Gold Writ + Lvl 3 O-Power: $172800
Champion Diantha stomps into the Battle Chateau with FOUR level 60 pokemon (level 80 with Black Writ). With so much experience and money gained from facing the champion, its basically worth it to spend all of your O-Powers and activating all the Writs for this battle.
Le Wow vs Battle Chateau
The Battle Chateau is far better for money than Le Wow. With only $200,000 investment for the Silver and Gold Writs and Amulet Coin, it becomes possible to earn $21,000+ per battle if you solely focus on the "old men" and "old women". With O-Power lvl3 stacked, you'll be earning anywhere from $63,000 to $150,000 per battle with proper opponent selection.
For experience, the Battle Chateau seems to have the edge as long as you can afford the $400,000 Black Writ and Silver Writ. However, the experience gained here is somewhat random. If you only have Rich Boys and Ladies to face, you don't really know if you're gonna be fighting a lvl 35 Ralts, or a lvl 60 Haxorus. Nevertheless, with proper "opponent selection", you can focus on Elite 4 (lvl 75), Gym Leaders (lvl 70), and Furisode Girls (lvl 60 and 65 Audinos) and gain a significant amount of experience points.
In the worst case, you may spend a few battles facing lvl 35 Burmys or Ralts, but within 5 minutes, the Silver Writ will flush out all of the trainers and give you a fresh new start.
Le Wow Triple-Battles / Rotation Battles on the other hand consistently offers lvl 63 Pokemon, and your O-Power for +Experience will last for all 5 trainers / 15 Pokemon. However, since you pay $90,000 to enter the restaurant, and only get ~$125,000 in profits after selling the Balm Mushrooms (with lvl 3 exp O-Power / Lvl 1 +money O-Power), I know for a fact that the Battle Chateau offers far more money than Le Wow offers you.
Finally, Le Wow Rotation Battles have a slow and annoying "level up" bar. Leveling a Pokemon from lvl 1 to lvl 15 takes but a single battle in Le Wow... but the amount of time lost waiting for the level bar to fill up is painful. While Le Wow Rotation battles offer significant amounts of experience points... my personal experience has me shying away from them, especially when raising baby-level Pokemon to higher levels.
After all, once you pay the $200,000 for the Silver and Gold writ, the Battle Chateau doesn't require any more investment until midnight. You have to pay $90,000 per Le Wow visit.
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