Well, I hope we can all agree on one thing: Spider-Man Web Swinging >>>>>>>>> Arkham Knight Batmobile Driving
Batman's stealth is better, naturally, and there's more of it, as there should be. Vice versa with traversal, Spider-Man's moving about the open world is just better. I think Spider-Man's combat is more about tactics and preparing one's loadout to a given style, where as Batman's combat is more an even skill test, just with new toys to play with. It's hard to compare their combat, because they give me very different success feelings. I will say though that Batman seems a little bit badass even if you suck at the combat, but Spider-Man doesn't.
I think the open worlds of these games are different. Batman's is almost a psychological landscape, whereas Spider-Man's is the man on the street. The details in Spider-Man are guys on the street dancing on cardboard, but the details in Batman's are like a leftover doll from Ventriloquist hidden by the Riddler or something. There's a lot more mind in Batman's world, but there's honestly so so much more heart in Spidey's gameworld. It feels like you stepped into a real place, and not just into a comic book panel, not that either are anything to sneeze at, but Spider-Man lives in a living breathing city... he has non-combat interactions. Batman doesn't really.
Honestly, I like Spider-Man's detective mode better, it's limited to something that makes sense for the character, unlike Batman who suddenly developed X-Ray vision which made no sense to ever turn off. Batman's detective mode is overdone, imho. Something more like Spider-Man's which highlights things that the Sherlock Holmes mind would pick up on feels more heroic and less game-y to me.
In the end, Arkham City is the best of the Arkham games, and I don't know if it goes above or below Spider-Man. It seems on par. Different strengths and weaknesses. Overall, Spidey has more heart, and Arkham has more brains.
But I'll tell you this, Spidey is building on what Arkham has done, and they are still building and have the general advantage of being later in time. After MSM2 comes out, I don't think there'll really be much of a comparison. So I'd put money on:
MSM > Arkham Asylum
MSM2 > Arkham City
MSM3 >>>> Arkham Knight
Marvel Spinoff made by another studio > Arkham Origins