No, no. It's not what you think. This is pure fantasy fun. Imagine almost 20 years back, at the end of the JLA/Avengers crossover epic, in an effort to meet the possible threat of enemies crossing from one comic universe to the next, the JLA and the Avengers decide to create an ultimate team comprised of the best of the best from both teams. In this instance, the best from the Avengers and the best from the JLA. Additionally, other heroes from all teams from each universe may be included to provide relief for the primary team upon recommendation from two team leaders, or they may simply be included in the main team! Likely, this should include one leader from the Avengers and one from the JLA. The resource teams, aside from the Avengers and the JLA can include (but are not limited to): Fantastic Four, X-Men, Defenders, Champions, Squadron Supreme, Green Lantern Corps, Legion of Superheroes, Justice League Dark, Teen Titans, JSA, etc...
Also, if you are daring you may include one or two villains from each universe if you think the gains from their addition outweigh the risk of their inclusion. Finally, drawing on the energies of the power cosmic and the speed force as channeled through technology created by Reed Richards, everyone's powers work exactly as they would normally in their respective universes (I threw that together...if you can think of something better, by all means, go nuts!).
Tell us, who would you like to see on the team? Maybe we could limit to 10, maybe 12, total team members? Who knows, maybe Marvel and DC wouldn't mind giving another shot at collaboration between these two iconic teams...