Batman: Arkham Asylum was just about a perfect game. The story was great, the combat was fun and unlike any other game’s combat, and the game didn’t overstay it’s welcome. Arkham City is not a perfect game, but it’s pretty darn good.
I’d say the story in this one is even better than the story in the game’s predecessor. The combat has been improved. Now you level up, and can learn new combo attack moves.
Unfortunately, moving around in Arkham City is a bit cumbersome. There are some weird things about the city itself. For example, the police department doesn’t even have a front door. You have to go in a side entrance. In fact, their pretty much isn’t a straight way to get to anything in Arkham City. You zigzag to get from location to location.
There were a couple fights that were unreasonably difficult. But all in all, the combat was enjoyable. The end of the game was a satisfying conclusion. Hint: Joker doesn’t actually die. I recommend Arkham Asylum over this, but if you played it and find yourself wanting more, give Arkham City a try.