Well, there have been crossovers that show the two universes co-existing on the same Earth-- 2 Superman/Spider-Man team-ups, Batman/Hulk, X-Men/Teen Titans, Darkseid vs. Galactus. The second Superman/Spider-Man team-up, written by Jim Shooter, actually does have Clark going to work for JJJ and Peter going to work for Perry.
The JLA/Avengers team-up shows the two teams in separtate universes as does the Marvel vs.DC minis. The Marvel vs. DC minis actually briefly merged the two universes into the Amalgam Universe.