Bigger world, better combat
The scale of the world seems much more massive, and the combat is more refined and intuitive.
I found the story excellent; some have complained the main plot is too brief, but there's so many side quests and riddler trophies it's not like there's a lack of stuff to do. Plus, probably the funnest element is just flying/grappling around Gotham taking out punks.
The graphics are as good as it gets for the PS3. The sound is beyond excellent and the voice acting is better than most Hollywood movies. The gameplay is refined, and although I am not a puzzle guy they're pretty intuitive.
If you like action games with a bit of puzzling and a lot of exploring, this is the game for you.
I mean come on: you're batman!