Depends, in MVS3, Captain America sucks (or at least when I use him)
Anyway, I think that Spiderman would win. Captain America would put up a good fight, but he has a shield, and Spiderman has web fluid that could jank it from him. Even if Spiderman couldn't, Captain America wouldn't be able to hit spiderman because of Spiderman's spider sense.
Now, Captain America is a smart boy, and would probably study up on Spiderman first, he would try to reason with Spiderman for whatever reason they are fighting. Peter Parker, being the sensible kid he is would make a smart comment and then probably calm down.
If one of them were possessed, than by the law of Comic Books, the other would win. No matter how bad the odds are or how one of Dr. Strange's nemesis's gained control of the superhero, the latter would always beat the super powered former.
So the final answer is; TL

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