This line of thinking always bothers me. You're telling me that a team with
two demi-gods, an Eternal, the greatest tactician in the universe (as acknowledged by several sources), more than its fair share of bona-fide super geniuses, and (on several occasions) the Incredible Hulk as members is underpowered?
Granted, the JLA has none too few heavy hitters, with three characters in the Superman-class. However, of the usual big seven lineup, only the Flash (Wally West) imbalances things in favor of the Justice League. I'm as big a fan of Big Blue as anybody you'll find on these boards, but Thor has him just beat out (for the same reason that Captain Marvel should beat Superman: when all other physical stats are equal, magic will give them the edge against Superman). Wonder Woman and the Martian Manhunter are also incredibly powerful, but if the Avengers lineup in question is packing the Hulk and the Sentry, it essentially takes the "big bombs" out of both teams for the duration of the fight.
Captain America will beat Batman eventually. Yes, they start out about dead even, but the Super Soldier Serum coursing through Cap's veins keeps his body from being fatigued. Batman doesn't have that. So, in a prolonged engagement, Cap should take Batman down.
That leaves just the Green Lantern against whatever else the Avengers can throw at him, and that's going to be a tough job for anyone with an Oan power ring.
Now, don't ge me wrong, this did require an upgunning for the Avengers and a degunning for the JLA (as the Flash is almost unquesitonably the most powerful member of the League). Any way you cut it, though, a matchup like this is going to depend on the lineup of the teams involved. Even taking teams at their absolute peak of power (the Avengers having King Thor and the JLA having Superman One Million), it's really more of a stalemate than anything.
And besides, you woudl in fact need two "Earth's Greatest Heroes" for two Earths, right? So why can't everyone get along?
(Really enjoyed that part of JLAvengers)...