Are they fans of both Marvel and DC characters?
They seem to be fans of both Marvel and DC characters, but we see more DC characters than Marvel ones.
In the S03E13, we see Sheldon agreeing with Raj's request after getting a pair of Hulk Hands signed by Stan Lee. There is also appearance of Stan Lee in S03E16, where he comes to a comic book store to give autograph on comic books. That's when they discuss about the comic book they want to get autograph on. And in one episode, Raj dresses up as Thor.
These are just a few examples of Marvel and there could be more I might have missed. However, the thing is we see DC characters having more appearance than Marvel ones.
Since the show is owned by Warner Brothers, who apparently also own DC comic, we see more DC merchandises and characters in that show. For example, Sheldon wears Flash tshirt many times, they do dress up as Justice League for new year eve costume contest, discussing about scientific accuracy of the dive by Superman to save a lady etc.
This can be a copyright issue to show a Marvel comic book since they don't own it, which is also a reason why we see a few Marvel characters. However, it's really never been stated in the show or by the crew that who are they fan of most.