Spider-Man would likely beat Joker, through it depends on which version. Joker's plots usually only work because Batman's a bit of a dummy and doesn't (or can't) have his eye on Joker 24/7.
Joker's plots are also very specifically sorted for Batman's morality and tech: which doesn't really work against Peter, who's a whole different beast.
What advantage does Spiderman's morality have over Batman? He seems like he has a lot to lose compare to others and the death of Ben and Stacy seem to keep coming up.