depends what kinda badguys r in the city...
most of batmans enemies in gotham are non powered humans like him...except his has teh advantage of money, gadgets, and information along with element of surprise and planning. on top of that he's in better shape than most of his opponents. with the exception of low level brutes like clay face or bane..which spiderman can easily out smart or over power.
spider-man's enemies are usually stronger than he is, or at the very least as strong. so the strength is negated and he has to outsmart them as well. if a killer like carnage was on the loose, i'd rather have spider-man be in the city...joker, 2face, penguin, riddler, n madhatter really wouldnt scare me. realistically the police or army can kill them by brute force or by numbers..but they're usually inept in comics.
i think spiderman would fit in both cities since it's like a step down, batman would have more of a challenge fighting spidy's enemies. i'm sure he can do it. but the vast majority is stronger or deadlier than clayface or bane.
so it's pretty much on thugs vs super powered villains. in real life i'd worry more about a real carnage or venom than a real mad hatter/joker or mob boss.