One of the best games this generation, bar-none!
Absolutely fantastic Batman game that manages to beat the first one, even. There's just so much to do, explore, and find. And the way Batman moves around the city with the glide-cape and grappling hook combination is just so satisfying to use. So much comic-related goodies to find and unlock, too. It really pays a lot of fan-service to fans of the Batman comics, including lots of Batman's Rogue's gallery showing up to face off against. Plus you get to play as Catwoman and Robin, as well. And oh man, the graphics and general atmosphere the game protrayed was so Gotham City...so Batman. It was fantastic!
However, the one area where Arkham Asylum was better, was the storyline. Asylum felt more tight, focused, and story-driven; and it really felt like I had just read a great Batman graphic novel, when I was finished. Arkham City still had a great Batman tale to tell, but it wasn't as tight and focused as the story was in the Arkham Asylum, so it just didn't come off as impactful.