but marvel dont?
To my knowledge, the only character DC has any legal issues with is Superman, and that's mostly cause it's pretty well known that DC screwed over Superman's creators, Shuster and Siegal, with their respective heirs separately trying to sue DC for quite some time.
Below is the latest development on that.
Terrible grammar aside, both companies have had creative legal issues with characters in the past. There was the Superman/Captain Marvel thing that was pretty big. But they are constantly gaining and selling rights to other publisher's characters like the Milestone characters, T.H.U.N.D.E.R. Agents, and the Red Circle characters and stuff.
And then there's the whole Superman/Siegel family rights debacle. I think that comes with the territory of having a company that deals with creative rights to ideas. I know Marvel has had problems in the past with stuff like this too, it's not only DC.