That's more than one question. It depends on what you mean by best, to me... the best are the ones that successfully transfer the spirit of the character from stage to screen. So for me, The first Superman movie and the first Spider-Man movie are tied, although Iron Man comes in a close second.
I don't think that either Marvel or DC characters look better than each other on the screen or in the comics. There are characters that look better than other characters but I don't see that the publisher makes a difference in that.
I won't even try to answer which character has the best story to tell. If they didn't have good stories to tell they wouldn't have been published and put on radio, TV and movies for as much as seventy years.