Much better than Arkham Asylum and is awesome.
The good things:
The story is great, combat is enjoyable and satisfying, the open world impressed me is enjoyable see batman flying, the detective mode is better, playing as catwoman is fun as well robin (well he is only playable in challenge maps), and much like other open world games, it have secondary missions, but is your decision if you want to play it, these missions are not necessary to complete the story, the boss battles are great, I decided no say much information becuase I don't want to spoil everything.
The bad things:
Nothing.
In conclusion this game you must buy, even if you are not batman fan you will love this, thanks rocksteady for make an amazing batman game.