Spidey, I just wanted you to know that before you were posting here, I filled the roll of the Friendly Neighborhood JGlass. My sig was John Morrison with a Spider-Man mask on because he had just done that awesome spot at the Royal Rumble where he parkoured the wall and jumped back into the ring.
But anyway...
I'm also rolling with Spider-Man here. As displayed in Captain America: Civil War, even an untrained Peter Parker has the skills necessary to disarm Captain America, and once Captain America is without his shield this boils down to a fist fight. With better speed, reaction time, durability, and strength, Spider-Man would win.
The only thing Captain America has on Spider-Man, as far as I see it, is that he could probably assemble a plan of attack quicker than Spider-Man could. Cap has one of the best military minds in the world, and he'd quickly be able to determine the best plan for dealing with any foe.
Unfortunately for Cap, in this case the best plan of attack would be retreating until he can find someone to help him.
Vote Spider-Man