Just finishing off the Arkham trilogy.
Asylum is the most coherent of the lot, due to the smaller, confined nature of it. It feels much more Batman than the others, even if the gameplay isn't as refined.
City is all over the place. I think most of its popularity was due to "More Asylum!" and some refined controls in combat. But the story was a mess, the side missions not compelling, and it really ended far too quickly.
Knight has a horrible reputation because it was shoved out the door half-baked. Going back to it years later with all the patches and DLC; it's far better than City, even if it loses the great atmosphere of Asylum. I actually felt like cleaning up the city after I was done the great main storyline. Naturally I can't possibly make the time to do all the Riddler nonsense. They even joke about it at the end of Catwoman's story - "He can stay down there".