Kakashi would walk all over Spider-man even with out the sharigan eye. At very worst he has Quicksilver-esq speed and best... he cuts through lighting bolts with a jitus the requires both hand seals and charaging time. Not even a contest.
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Two of my favorite characters and you pit them against each other? D:
Is it a straight combat fight*i.e no genjutsu or ninjutsu, only physical techniques as well as no webs* or is it anything they have?
If it's straight combat, Kakashi barely squeeks ahead. The Spider-sense and Spideys new speed might give him enough of an edge to keep up, but it'll be hard to hit Kakashi hard enough to lay him out.
If it's all techniques and weapons(save for death I imagine) Kakashi wins rather easily.
Well since Spidey doesn't use any jutsu, just regular fighting moves, Kakashi isn't gonna be able to psyche him out and copy him. So I say it'll be 5/10.
Second battle, Kakashi has the advantage with lots of stuff to replace with. I give it to him definetly. 8/10 at least. Although one lucky spider-sense and a solid punch will put Kakashi down.