The actual comics: I pick DC as the winner. I haven't been buying comics lately, just reading older issues. DC's stories and characters just resonate with me, more. Superman is considered the first super-hero (debateable) and DC is considered the first universe. Sadly, as much as I love comics, I just can't afford the hobby anymore. It seems like comics are dying (with readership dropping and Wizard Magazine shutting down) despite comic movies being more popular than ever.
Characters: I LOVE Captain America and Daredevil. I like Wolverine, Iron Man, and Spider-Man but, up against the icons like Superman, Batman, Wonder Woman, Aquaman, Flash, Captain Marvel, Green Lantern, etc., they just can't stack up. Marvel characters are supposed to be easier to relate to but the way writers write these days, DC characters hold up, too.
Movies: Hands down, Marvel. DC has managed to consistently fuck up film properties like Steel, Superman, Green Lantern, Jonah Hex, and others. Meanwhile, Marvel has been dropping back to back hits with movies that just aren't good comic book movies, but good movies in general. Blade, X-Men, Spider-Man, Thor, Iron Man, Hulk, Daredevil.....even when the movies don't blow me away, there's no denying that I've had a good time. DC movies tend to be waaaaay too serious. Haven't seen Green Lantern, though (looks like its based on the Secret Origin comic. Looked pretty true to the source despite the poor reviews. The comic was great, at least).
TV: DC, easily. I watch DC shows like Batman The Animated Series, Batman: Brave and the Bold, Justice League, and such. I'm consistently blown away by the quality of the writing and the stories. When I watch a Marvel animated TV show, they just seem simplified and dumb. Look at Super Hero Squad, Avengers, the 90's X-Men and Spider-Man series, Fantastic Four, or Silver Surfer, Iron Man, Hulk, or what have you. With the exception of X-Men Evolution, they almost always are mindless crap. DC seems to put more heart into their TV shows (as well as little nods to people who only read the comics). Look at Batman: Brave and the Bold. There was an episode where Superman went bad. He yelled at Lois "Serves you right for all the times you tried to trick me into marrying you!" Lois said "I have no idea what he's talking about." A lot of people won't get the joke but it's based off of an old Superman (is a dick) comic book cover!!
Animated Movies: Again, DC. Marvel is trying a little harder with their animated movies and Hulk vs Wolverine was too awesome. Same goes for Planet Hulk. But if you compare the whole Marvel animated product line to DC's animated movies, there's no denying which company is consistently pumping out the higher quality features.
Video Games: Marvel has consistently been pushing video games that are, at least, decent. Hulk: Ultimate Destruction, X-Men Origins: Wolverine, Spider-Man, Ultimate Alliance, etc., these games are pretty good! They've been good for a long time. Only recently, did DC get their act together and push out the awesome Batman: Arkham Asylum game. While Batman single-handedly beat every Marvel game, ever, it's just one game. One great game doesn't beat several good games. Marvel wins.
While both are great. I just prefer DC.