I like this game, but so far I would say Arkham Asylum is the better game. It's more focused, the set piece were far superior with much more impressive level design. The guided structured level design makes for more polished gameplay and mission design, and I didn't know I'd be saying this about a Batman game but it just seems to work better that way. I really, really miss it. The Riddler puzzles are better here, for sure, but other than that... it feels like a step back. Or at least, it's a much "different" Batman game and I'm not sure it's what I wanted. I liked getting to an area in the previous game and knowing this is "such and such's place", and then having to go through really sweet set pieces with immersive, detailed and layered levels. In this game, much of that is pulled back. Areas belonging to specific enemies aren't as impressive. The city itself is "impressive", but I think it's missing that punch of the individualized areas of the first game which seemed far more meaty.
I don't know maybe those areas begin to expand and become more impressive with later game missions, but the early game story content is very disappointing. Story/Enemy specific areas are much shorter, less involving.
It's by no means a bad game, and the combat has been improved definitely and it's fun... but I just think I prefer the previous games structure more. It's a preference and I think I hope for Arkham City/Asylum 3 they go back.