City >> Asylum >> Origins >> Knight.
All are great, though I'll always be salty over Knight because of all the things it disappointed me with. Barely any thematic connection with the "Arkham" stories of the past games and dropping the ball on most of the insanely cool things City were teasing post-game... Plus, I'll never get over how terribly incompetent all of Batman's allies were made to be. I'll give it this though: They gave me one of, if not my favorite version of Jason Todd's "resurrection" story. Also, were we seriously supposed to just go along with Deathstroke and Firefly not changing their gear after 10 years? And Deathstroke, one of the world's deadliest assassins, deciding to fight Batman via a freaking tank? Jesus... The Batmobile was a lot of fun but we were forced to use it far too often.
Origins was so good but plagued by bugs and some poor level design. Despite all that, it had, in my opinion, the best story, boss battles, character designs, and music. Plus, the crime scene investigation was awesome. It's a shame they made one really bad choice there though, immediately highlighting the evidence as soon as you scrub through it. That made it way too easy. Instead, they should've let the players find the evidence themselves by actually identifying and selecting it, rather than automatically highlighting it for them. That would've made such a big difference. Aside from that, I suppose a big part of my disappointment with Origins was how similar it felt to City, though that's not unexpected given that WBGM had to work with the existing assets of City. Still, overall a damn good game.
City and Asylum are both among my favorite games of all time. I've made plenty of fond memories thanks to those games, and I've sunk so much time in their challenge maps. The Iceberg Lounge map is probably still my favorite. Both games had incredible atmospheres but of different kinds thanks to the sizes of their respective maps, so you'd get a unique experience with whichever you chose. Traversing the skies of Arkham City was just something else. It felt like the perfect size for me, not too big but big enough to give us so much to explore and discover. Unpopular opinion, but those 300 or so Riddler Trophies and challenges were all so much fun to collect and solve. On the other hand, exploring Arkham Island was a fantastic experience thanks to the almost claustrophobic atmosphere it gave. Even outdoors, it really felt like you were trapped there. Which is of course entirely appropriate given that Batman is trapped there. Uncovering all the secrets the island was hiding and unlocking new areas here and there after getting new gadgets and upgrades... ahh, such a great game.