So I played the first Batman game through because I wasn't sure if the story was going to lead into Arkham City and I thought maybe there's tricks you'd learn in the first one that they would assume you just know in the second.
This game was pretty good. The aspect I liked most about it was the stuff like a Hitman game where you have to sneak around and take down a room full of baddies all stealthy.
The brawler aspect of the game was okay, but the control system was a bit too simple and lacked control at times. I couldn't always predict which way Batman would go, I would just press 'strike' and the computer would pick which guy it wanted me to fight next. This was annoying in stages where you are fighting a bunch of thugs and a big guy occassionally rams through because I would end up in his path even though I wanted to fight a guy who wasn't in his charging path.
The game was fairly short, but that was probably a good thing because it was pretty repetative. The Batmanishness of it was excellent. I am not a big comic book guy, but I did enjoy all the fun trivia stuff. And they worked in lots of good characters.