I think it has a lot to do with where both companies started. DC goes all the way back to the 1930s, when it was just pulp entertainment done by hacks for little kids, kind of like 80s cartoons, with the exception that there were some moments of accidental genius, like Jack Kirby. Marvel also existed then (as Timely Comics), but was a relatively minor company.
The real genius of Stan Lee in the 1960s was to combine superhero comics with romance comics, and elements of melodrama and realism, so characters like Spider-Man and The Fantastic Four seemed to have "real-world" problems. DC, by comparison, was going in a more space-age sci-fi direction, with high concept stories featuring wooden characters like The Flash, Green Lantern, and Adam Strange. Marvel's breakthroughs at the time became a bit of a countercultural phenomenon, with teen and college-age baby boomers identifying with underdog heroes like Spider-Man or The Hulk. Eventually these breakthroughs made stuff like Vertigo and "deconstructed" superheroes possible. Actual art comics for adults, Fantagraphics-like stuff, are more influenced by newspaper comics, fine art, pop culture, European comics, and 60s underground comix, but you can see some mainstream comics influence in the work of creators like Dan Clowes and Jaime Hernandez.
Today the big comic companies are indeed like sports teams, in that mercenary talent rotates between them -- the only difference between Grant Morrison on Batman and Grant Morrison on X-Men is the character background and brand identities he's working with.
