I would say Asylum by a hair. While City has the better gameplay, Asylum has the better story and atmosphere. While they're both top-notch games, I find myself replaying Asylum more than I do City, and for that reason I vote Asylum.

On a related note, I'm worried about how Origins wil stand up to Asylum and City. This will be the first Arkham game without Rocksteady, Dini, Conroy or Hamill.

This was an extremely close call.

I'd say Arkham City by a hair. I do think Arkham Asylum has the better atmosphere and a less convoluted story, even though AC had the better ending, but City improved the gameplay by a lot by adding gliding, extra weapons, sliding, improving detective mode, and enhancing the riddler challenge. The only thing lacking in AC was the Scarecrow hallucinations. Although there were times where Batman would hallucinate in AC it wasn't as amazing as it was with the Scarecrow nightmares. AA was a more psychological game, and the interview tapes were better in Asylum also. Arkham City managed to improve upon just about everything else. The Challenge Rooms in AC was an improvement as well, especially with the inclusion of Robin, Nightwing, Catwoman, and all the alternate costumes. Arkham Asylum did have a playable Joker mode though (at least for PS3). So yeah, I vote for AC but it only wins by a hair, mostly because I like how the gameplay evolved.

I am worried for Arkham Origins as much as I anticipate it. It is indeed a new developer and there will be no Conroy, Hamill, or Dini. The lack of Dini worries me the most. The new developer kind of worries but at least they'll be using basically the same gameplay engine that Rocksteady used. The lack of Conroy is because they want a younger sounding Batman. The lack of Dini is unacceptable though. Arkham Origins may end up with a shit story due to that, but I hope I'm wrong. What I know about the story so far isn't very Arkham-ish as it involves 8 assassins, including Deathstroke, being hired by the crime boss, Black Mask, to eliminate Batman and it takes place in a snowy Gotham City kind of like AC except it wont be a big prison. I don't expect the atmosphere to be as surreal, but I wont doubt Warner Bros. Montreal will try their best to scare the player by making the villains ultra violent. I certainly don't expect Origins to be better than City or Asylum. I just hope it's at least more enjoyable than "The Dark Knight Rises" in terms of story, and that the game-play isn't too stripped down since it's a prequel taking place during Batman's 2nd year as a vigilante, before he was as refined.