I like both, but Marvel more than DC.
Typically, Marvel characters have very human flaws, which give them depth. Sure, Bruce Wayne's parents were killed, and he decided to become Batman to rid the world of scum that would do that. But let's look at Peter Parker/Spider-Man. Uncle Ben--his father figure, his hero, his role model--is killed by a similar thug, but this time it's not just chance like it was for Bruce. No, this guy got to Uncle Ben because of Peter's own selfishness, his desire to get back at someone who wronged him. Tony Stark is an alcoholic. Hank Pym is a wife beater.
My favorite, however, is Doctor Stephen Strange. He was a highly skilled neurosurgeon. Top of the line. Simply put, it went to his head, and made him an arrogant bastard. He then gets into a car accident, and suffers severe nerve damage. His hands now useless, he searches desperately for someone who can repair his hands. His travels bring him to meet the Ancient One who ultimately teaches him the mystic arts, and eventually leads to Strange become planet Earth's Sorcerer Supreme. Basically, I like that fall Marvel heroes go through. He had to lose everything before he could become greater than he ever was. That line of thought has actually gotten me through some tough times in my life.
All that said, I do like Green Lantern, Batman and Watchmen.