There's no question that both companies are very successful and has a plethora of superheroes under their wing with memorable moments attached. But of all the years watching cartoon shows and live actions movies based on both comic companies, I'm noticing a pattern of which where each excels at. Surely, the directors, writers, art direction, etc... tend to determine which companies can produce better mediums, but overall, I think there's a fitting motif to it all.
So the arguments I'm going to make are the following:
1. When it comes to animated shows and stores, DC eclipses Marvel in this respect. I say this because looking back in my childhood, and even to this day, I find many of the shows on the DC side much more compelling in terms of character, story, and quality. Whether we're talking Justice League, Batman: The Animated Series, Superman, and even to a lesser extent, the many incarnation of the Superfriends. Yes, I did watch and love Spider-Man and X-Men, and even to this day enjoy them, but they don't have the same kind of lasting appeal to me.
2. Marvel truly shines when live action shows or movies are involved. I have to admit, Spider-Man movies, The Avengers, and even the X-Men movies to a degree are leagues better than what the live action DC movies offered to the audiences. I really enjoyed the Tim Burton Batmans (first two), but I couldn't understand the hype behind the Christopher Nolan renditions of them. I find the Dark Knight trilogy severely overrated and tries too hard to come off as something compelling [and don't get me started on Heath Ledger]. The Superman movies were a hit and miss, but overall, not quite memorable.
Conclusion: DC beats out Marvel in animation, whereas Marvel beats out DC in live-action shows/movies.