I don't watch any of the more current Marvel/DC cartoons (though I did see one episode of Justice League Action and liked it; saw an episode of Agents of SMASH and hated it), but as a general rule, DC has always had the superior animated TV/movies going back decades.
Marvel had a lot of really, really bad cartoons in the '90s, spreading themselves too thin with FF, Hulk, Iron Man, Silver Surfer, Spider-Man/Spider-Man Unlimited, X-Men (which isn't terrible, but hasn't aged well and fell off hard after the first two seasons or so) & Avengers: United They Stand. DC focused on quality with Batman: TAS, Superman: TAS, and Batman Beyond. DC had the best cast & crew and the best TV animation studio backing these shows.
To me, Marvel's best cartoons are Spider-Man & His Amazing Friends, Spider-Man (1981) and Avengers: Earth's Mightiest Heroes. EMH was amazing. Still mad they canceled it for Avengers Assemble, which is okay, but EMH felt like a classic superhero cartoon.