Well first off, i love all these versions of Batman. Each one was great in its own way. Asylum is the most like the animated series imo, with a good portion of the comics thrown in. City is the most like comics (80s and 90s specifically). And the look, feel and atmosphere of Origins is the most like the Burton movies. Knight seems the most like the Nolan films.
Asylum is my favorite of the three. Its tighter, smaller, Metroid-like layout really suits batman i think. And even though i love big, open world games, sometimes you get a more detailed and richer experience when everything is more confined. I also have a thing for spooky mansion/castle/asylum type places as compared to city buildings. I also loved the look of the characters the most in that one (especially Batman and the Joker). And finally, exploring the island and finding out about its history was so interesting to me. I didnt feel that with the other two.
City was awesome in its own right though. It was so gritty and dark, it truly felt like Gotham. It also made me really feel like the Dark Knight, using the rooftops to hunt for bad guys. Id say over all, it was a more epic game.
Some people didnt really connect with Origins, but i definitely did. I prefer Gothams look and feel a bit more in this one than in City. I think the Christmas setting has a lot to do with it. I can tell the new team put a lot of love and effort into this one and im thankful for it. Gameplay wise, all three were very similar and thats not a bad thing to me. Each one was fulfilling and fun.
I am suuuper excited for Knight! It looks amazing! And while it appears to be huge, it also seems like it has some of that deep richness Asylum had. The only two things im not overwhelmed with happiness about are the looks of the characters (they seems a bit funky and weird to me) and the possibility that playing in the same setting (big open city) might get old after a while. But again, i think it will be an all around incredible game. Cant wait to get my hands on it!