I'm not really a comic fan, but I got into the spirit of being the Bat-Man. The designers did a good job of emphasizing mobility and stealth over straight-up combat madness. And it's occasionally thrilling to zip along a bat-grapnel or hang-glide silently with the bat-cape.
Of course, it'd be nice if the Bat picked up all his freakin' bat-equipment the first time he bat-arrives at the bat-cave, but that also serves as a clever-yet-infuriating way for the designers to slowly provide more access to new locations as the game progresses.
The basic game is plenty fun, even if it ultimately boils down to knocking lots and lots of people unconscious. The highlights for me were a few hallucinatory interludes courtesy of the Scarecrow, who preys on Batman's particular psychopathy. The game even briefly breaks the fourth wall (or however many walls a videogame has) in a cute bit of mindfuck (spoiler).
I would also be remiss if I didn't mention the Riddler, who has strewn trophies and riddles all over Arkham Island. Many are just little trophies like the hidden treasures that Lara Croft finds in nearly-inaccessible places all over the world. Others are riddles that require Batman to take a picture of the solution. Sadly, some are solvable by using the strategy 'take a picture of anything that looks different from the endlessly repeated wall panels'. But others are more fun to hunt down.
Good clean fun. Pow! Biff!