I think you've drawn from too small a sample size. Perhaps the movies only?Some back stories are just more interesting, eg, Wolverine, Spiderman, Darkman, Magneto, Iron Man.
But of course, not all Marvel characters are so inspired, eg, Thor, Captain America.
But other than Batman, DC guys & gals share the super power of inducing sleep.
Hawkgirl's depiction in the Justice League series was one of the most interesting characters, imo. I loved her character when I was watching that show as a teen. She totally breaks most female comic stereotypes, and eventually is revealed to have been an agent for her own race (rather than being stranded from her race, as previously thought) to scope out earth. But unknown to her, the reason to scope it out was to destroy it. So she ends up being viewed as a traitor by mankind, and by her love interest John Stewart (one of the Green Lanterns), and she fights against the Justice League, until her conscience gets the better of her and she has to be a traitor to her own people and help the humans. But her race had to destroy the humans to live themselves, so their civilization was wiped out because of her betrayal, which she had to deal with.
Plus in that show they had Green Arrow and Black Canary characters, with interesting and well-acted dynamics between the two. They were good for episodes where they wanted to focus on less-powered superheroes.
So DC has some pretty good backstory characters other than Batman. Their movies tend to focus on the lamer ones. (I was corny enough to watch superhero tv shows as a teen like the Justice League, with a particular interest in the romance between GL and Hawkgirl, and Green Arrow and Black Canary, probably based on my age and interests at the time.)