Both, definately.
I love both's movies (Bar Superman, hate him. Too super), and the characters I know of.
I'm a little more leanient toward Marvel, because... well, X-men, Spider-man, Hulk, Iron Man... Marvel's fucking iconic. EVERYONE knows their characters.
Sure, people know Batman and Superman too, but ask a random person how many characters from each they know of. I bet they'll know more Marvel.
But on the other hand..
DC made Watchmen.
That is all.