Superman alone against the the entire Avengers? That's suicide! Thor alone can handle him. Sentry can take him alone as well.
Superman knocking the Hulk out in a long fight? Impossible! Superman needs to give his all early on to prevent Hulk from getting stronger and stronger. If he fails to understand this, he'll lose.
As for JLA vs Avengers, I think the team who will win is the one with the best battle strategy.