Thought about it for a bit. Spidey wins round one, Bats wins round two, third round??
Spidey, because, ultimately, Spidey is stronger, faster, and smarter. Bats may be the better detective, but SpideMan designed and built his own web shooters. Batman had others build that kinda stuff while he honed himself to be as fast and as strong as he could be--problem is, he's not fast enough, or strong enough to be able to compare to even half of the speed and strength Spidey has. Once the gimmicks have been brought out and countered it would come down to a fist fight, and Spidey would only have to catch Bats in the face once to put his lights out--it wouldn't be easy, cause Bats fighting skills are greatly superior to Spideys, but, Spideys fist would be the Marvel vs DC version of the golden gun from N64's GoldenEye.
Lol, that's how I see it anyway