Spider-man vs Batman villains, Batman vs Spider-man villains.

I think Spider-man would do very well against Batman's villains. Batman usually studies his enemies and always finds a way to outsmart them to take them down. Spider-man is a genius too and after one or two mistakes will learn to take them all out. Joker won't be able to break Spider-man, he's lost people before and always came back stronger.
Batman would be the same, maybe a bit more efficient. Fear is an excellent motivator and he may even scare off his lower class villains for good.