Tough one. What are we referring to? Comics? Movies? TV shows? Cartoons? Video games? Because both excel in a certain category.
Well, excelled. Past tense. Especially for Marvel, especially since the MCU sucks (I'd argue it was pretty mid going back to some of their Phase 2/Phase 3 titles even), and I thought Marvel Rivals' just an overrated Overwatch (which I didn't like either), while DC has those Arkham games, The Penguin, Patterson's The Batman, and the upcoming James Gunn Superman. Spider-Man belongs to Sony, not Marvel, but I guess you could count those if you really want. I heard Daredevil: Born Again is good, but we'll have to see if Marvel fumbles the ball on that one since it only recently aired.
I guess my point of view comes down to the fact that I grew up on Marvel, but as I grew older, I just much prefer DC stories a lot more. A lot of Marvel media outside of the comics tend to be more family-friendly. The comics are a different matter, but you also have Watchmen, The Sandman, V For Vendetta, The Dark Knight Returns, Kingdom Come, Superman: Red Son, The Killing Joke, etc.
Marvel's got their own bangers when it comes to the more sophisticated stories too, don't get me wrong; I am a Spider-Man fan after all. Kurt Busiek's "Marvels" was a great one, as was Kraven's Last Hunt... That's about it that I know of though. Maybe you can throw in X-Men too, I guess. I think it's because most of my exposure to Marvel comics is Spider-Man. Most of my exposure to other Marvel heroes is through their movies and TV shows, and those are obviously more kid-friendly than the Distinguished Competition.
My exposure to DC though is a lot lesser because I've never picked up a DC comic in my life outside of Alan Moore's stuff, but that just makes it funnier because I heard of those great stories like Sandman and Kingdom Come even though I've never read them. Well, I've skimped through them, and I mostly liked what little I read compared to anything Marvel I've read for the past 20 years. Even though I heard that Marvel comics are supposedly a lot more mature, DC titles just seem to be more sophisticated in terms of their writing with people like Grant Morrison, Frank Miller, and Alan Moore behind some of their best titles.
In terms of animation, DC wins this one. It's not even a competition. They've got Batman TAS and Bruce Timm, not to mention the entire catalogue of DCAU. 'Nuff said. Marvel's got The Spectacular Spider-Man and Greg Weisman, but they fumbled the ball on that one by cancelling it.
Live action television is a more even field for both of them thanks to DC being associated with CW, but they currently have the slight edge thanks to The Penguin, but Born Again might help Marvel catch up.
Video games, DC takes it mostly thanks to Batman, much like how Marvel's best games are Spider-Man games. The Arkham games are masterpieces compared to ANYTHING Marvel dished out in terms of gaming, period.
Long story short, DC media outside of comics are mostly for adults, while Marvel outside of comics is mostly for families. I much prefer DC. To be fair, I haven't picked up a comic book for years, so that doesn't help. I could only base my opinion on what I know, the TV shows, movies, and video games.
That being said, I think this also comes down to a "can't we like them both?" kind of question, because fandom rivalry can get... uh, toxic. Sure, DC's got plenty of great stories, but much like Marvel, they've got lots of terrible ones too, especially during the Silver Age (Silver Age Superman alone is cringe). And there are comic companies outside the Big Two anyway. For example, Spawn and Invincible aren't Marvel or DC; they belong to a little known company called... *drumroll* Image Comics. Then you've got the other companies like WildStorm and Dynamite too (both of which are partially responsible for "The Boys", so it's a pretty big ocean out there that aren't just The Big Two.
Don't even get me started on manga.