Not necessarily. In the Amazing Spider-Man series, he's an adult now.
Anyway, Spider-Man would win. Seeing as how Batman doesn't have much strength or agility, Spidey would be able to web Batman up and take away his gadgets and shit pretty easily.
are we basing this off of the comics or the movies?
probably the movies. if that's the case, batman. webs are useless against people with retractable knives that can cut through steel, batman's much more rounded as far as what he fights with, and spiderman would get his ass kicked in hand-to-hand combat.