I didn't play Asylum but I really wanted to like City except for the fact that GFWL decided I wasn't good enough for it's cloud and I played the first 20 minutes about five times before it felt I was privileged enough to have a save file. Then GFWL shut down and I lost that progress anyway.
I'm not sure if I'll give this one a swing or not, I found the gang melee combat to be a bit bland after watching batman flail around knocking in his 50th head from some rhythmic button pressing. It also made me suffer a bit from that open-world "urgency" where batman is more or less on a time constraint but the game wants to shove endless trophies and bat-tests down my throat while Bane wants me to run some errands for him.