Asylum. Both games are open world, but City is more open and one thing I really disliked about City is the grappling hook. The use of the grappling hook took away from the exploration in the game imo.
On City, except for the very first party of the game where you were doing the platforming like sections as Bruce Wayne, it feels like you're shooting your grappling hook everywhere to get around. If you were to drop down to the ground and explore everywhere on the city streets, you'd be required to use the grappling hook every once in awhile because there are too many dead ends or sections completely blocked off from the ground. in Asylum you actually had to explore everywhere. Throughout the game, in order to get to new areas you'd have to platform and climb your way up, shimmying around, jumping across ledges, etc. In Asylum you'd scale the elevator shaft, while in City, you'd look up and shoot a grappling hook.
The other thing on City is that when you get into a room full of thugs, you can grapple up to anything to get out of the way, while this wasn't possible on Arkham Asylum. On Asylum in every room with thugs, you could only grapple to the gargoyles if you needed to get away, but not any location. So the stealth sections were more about stealth as you'd have to also traverse along the same areas the thugs could be at.
The freeflow combat was also fresh in Asylum. It doesn't mean I like the combat any better or any worse, but while freeflow was unique at first, I didn't care for it in the later games because it's one of t hose I just got tired of after playing the first game. It's good just feels a bit too automated. Unfortunately it looks like Arkham Knight is yet again using the same combat.
The only thing that City has going for it over Asylum imo is the large open world with the new puzzle riddler trophies and the bosses. The bosses weren't all that great to fight, but they were better than titan after titan.
I haven't played Origins other than fighting Deathstroke on new game+ or hard mode. Got past him for a friend. The boss battle was imo better than any freeflow boss battle in City imo. While I didn't like yet another use of the free flow system which is the only reason I've kept from playing the game other than the online(which is really good,) enemies countering and being able to counter counters was really cool in that battle, though I know it's also elsewhere in the game also.
