Spider-Man is Spider-Man. Even in the Ultimate Universe, where Peter was officially portrayed as half as strong as he was/is in 616 canon and Captain America was explicitly superhuman as opposed to "peak human that often gets written as superhuman" in 616 canon, Cap was still portrayed as having a hard time overpowering Peter. Most versions of Spider-Man can lift at least 10 tons and are fast enough to catch up to speeding cars from a standing start, so from a physical stats standpoint, they would overwhelm Captain America in a fight unless distracted by inner conflict (like Peter was when fighting Cap in the original Civil War) or holding back severely out of fear of seriously hurting or killing him (like Peter, again). Captain America usually holds his own because he's a significantly better-trained and more experienced fighter, tactician, and strategist than most versions of Spider-Man, but if pitted against one that had no qualms about killing him or other internal conflicts derailing his focus and wasn't going to hold back for anything, he would be in serious trouble.