Hmm. Well, all things being equal, Aquaman would have the advantage of physical strength, speed, and stamina and his telepathy, which can work on other beings besides ocean creatures. Spider-Man knows New York well, and his spider-sense might make up some slack for being slower than Aquaman. Arthur is probably a better fighter overall, but Spider-Man has beaten quite a warrior enemies. On the other hand, in NYC, exposure to a water hydrant or the sewer to replenish Aquaman in a brawl isn't unlikely. It also should be noted that many of Spider-Man's victories over overpowered enemies came after some sort of dues ex machina; time to prepare some solution or serum, a conveniently placed wet cement foundation, etc. Most people even attribute the symbiote costume for his "punch and repeat" defeat of Fire-Lord way back. That or bad writing.
Barring such plot-centric breaks, I think Spider-Man would last longer against Aquaman than he should, but the most he should hope for is a draw, go the distance style. Aquaman doesn't have the rep, but he's no pushover. It also depends on how tough his webbing is, which is also dependent on the writer; in some eras, it was a struggle for even super-tough enemies to escape from, but since the 90's, it seems anyone above peak human can rip it easily. I just don't think Spider-Man can overcome the power gap without a retreat or some sort of convenient thing in the area. Draw or Aquaman victory, eventually.