What is the most balanced/competitive character set in Citadels?
I've found the default characters are the most balanced set of characters.  While I haven't played with all of the extra characters, some of them significantly change how the game plays.  Bruno Faidutti, the creator of Citadels, says he prefers the default characters on the game's Rules FAQ on his website.  Quote:


  Q: What is your favorite character mix? 
  
  A:
  The 8 basic characters, plus the Queen or the Artist when playing with 6 or 7 players.
  
  Q: What's the best character mix?
  
  A: 
  Many players prefer the Witch over the Assassin, but I disagree. The Assassin is simpler and naughtier. I prefer the original set, sometimes with adding the Queen, and sometimes with replacing the Merchant with the Alchemist.


For the extra characters I have played with, I have a few impressions I can share with you.

Tax Collector:  I found without the threat of the thief, people started hoarding money.  This reduces some of the tension in the game.  Since players can't get robbed, they can save to build up to build the most expensive district.  Players were also careful to not have money to pay the tax collector after building.

Emperor: Since you can no longer take the crown for yourself, most people gave the crown to the player to their right.  This gave them a better choice of cards in the next character draft, while benefiting the player to the right.  The Emperor does make it fairer though how the crown is distributed, but it's also the only character ability the benefits someone else in the game.

Alchemist: The ability to get all your gold back you spend is great, but the Alchemist replaces the Merchant.  Since the Merchant can tax green properties and the Alchemist can't, this makes green districts the most worthless ones in the deck.  They can't be taxed and provide no special benefit.  Green also happens to be the most common color in the district deck

Finally while i haven't played with it, the Diplomat seems to be one of the most powerful characters in the game.  It will definitely change the dynamic of the game and make it harder to hold onto powerful purple districts.  That doesn't mean that any of these characters are bad, and the opportunity to try them out was a bad inclusion in the game.  I just think the default set of characters is the most balanced.