See, the problem with a question like this, is that most people don't actually read comics. That means that what they see of the DC and Marvel universes is what makes its way to film, and honestly Marvel does win when it comes to film.
That said, when it comes to the original comics that they're based upon, DC is far and away the superior company. Batman, Wonder Woman, Green Lantern (all four of them), Aquaman, even Superman are all much more nuanced interesting characters than they're given credit for, because most people never see them outside of the medium they were intended to be viewed in. I spend roughly $80 a month on comics, and not a one of them is Marvel. They're almost all DC, because the stories that DC puts out are genuinely amazing. The connected DC universe is the largest fictional universe ever told, I honestly don't pay enough attention to Marvel anymore that I could expand upon that point, other than to say that if you're looking for what is essentially the largest most complex work of fiction in human history, you should look no further than the DC universe.
I suppose that for the casual reader, Marvel might have its charms. But for the serious comic book reader, DC is hard to beat.