Superman is literally indestructible. What can a shield do that a building to the face couldn't? Also, the Justice League has an extremely large number of members, most of which could defeat Captain America or Iron Man. The sheer amount of super-humanoids in the Justice league would send the Avengers away with their tails between their legs.
Iron Man is an incredible character with amazing powers and it isn't that simple to beat him. Thor is a God. However far Hawkeye is, he could pick each one off with an explosive arrow. Black Widow could take down a lot of the others with her SHIELD weapons. Captain Americas shield is literally impenetrable. And need I say anything about Hulk?
While you are correct about there being many members of the jla, superman is not a god, he is an alien.But Thor is a god and the Avengers have also had many members, including members from other teams, like the X-men. But really,I think they would tie because they would pretty much be fighting doubles of themselves.For example, Hawkeye goes to Green Arrow, Superman goes to Thor and Batman goes to Captain America.