Batman: Arkham Asylum was one of my favorite games.
I'm multiple hours (but not done) with RockSteady Studios new Batman: Arkham City, and it pretty much surpasses everything I dig about the first game, without losing the stuff that made that first game great.
It could be a little overwhelming if you're not big into games, and/or haven't played Arkham Asylum -- there's a ton of gadgets; I even find myself having to stop and look at all of the stuff available to me. But that's a good problem to have (teh Bats has teh gadgets, after all).
I do like that the rogues gallery is a lot more complex this time around. Less "muah-hahahaha!" and more "I haz motivashuns. I haz needs. I haz issues."
The "detective" aspect of the Greatest Detective in the World is also way better, and the side missions compelling enough to pull me from the main quest (though I could care less about the AR training opportunities).
All of this makes the game a lot more fun -- beyond the solid stealth-or-brawler-or-gadget-or-investigation gameplay.
I'm mixed on the Catwoman missions, but I think that's just me -- it's somewhere in-between "different"{ and "not-different" gameplay, and I don't seem to be transitioning well. She is fun to watch in motion, though.
And being able to play as 70s Batman, or the Frank Miller's Dark Knight? Awesome. (As a fanboy, seeing that latter bad boy in motion gives me goosebumps). I also dig that it's not just the skin that changes -- there are changes to audio and animations, too.
I'm not done with the game yet (Mainly because I'm jumping between it, Dark Souls, Uncharted, and Skyrim) -- but I'll be joyfully investing in this game for a long, long time.
(And apologies for my brief fall into the pit of can haz cheezeburgers cat-speak. Not sure what happened there.)