Would Marvel heroes join the Justice League? Or would they continue in their own groups, like the Avengers?
Both teams have changed rosters many times, so I'm sure there'd be some intermingling if they coexisted. Although the thing is, they both fill the same basic role in the superheroic ecosystem, as it were -- the all-star team that comes together for the crises too big for any one hero. So if the characters had coexisted all along, I'm not sure we would've had separate Avengers and JL teams, but one team that emerged as an amalgam of the two (pardon the expression). Either that, or one team would dominate as the heavy-hitter roster with folks like Superman, Captain America, Wonder Woman, Iron Man, Green Lantern, and Thor, and the other might be more a second-stringer team akin to the West Coast Avengers or Justice League Europe.
Like I said: Settle the Avengers/JLA thing once and for all.
One battle royale. Winning team gets to be the super group for the new uni. Losing team disbands and joins the winners.
I'm rooting for the Avengers. I hope someday to hear Black Canary cry out "Avengers Assemble!" (Probably hear it in all the alternate universes...)