Current live action movies wise - MCU is (Justice) leagues better than the DCEU (or DC Other Worlds or whatever they're calling it). So far, it's not even close outside of one win with Wonder Woman.
Cartoon wise (movies, shows) - DC is on the whole beating Marvel by a landslide. While Marvel has had great shows like Spiderman the Animated Series, X-Men The Animated Series, and Spectacular Spiderman - DC has given a predecessor to the MCU in the DCAU which ran from Batman the Animated Series through Superman the Animated Series through Batman Beyond through Static Shock and culminating in Justice League/Justice League Unlimited, all of which (especially Batman, Supes, Beyond, and Justice League) were amazing, and add in Young Justice (GREAT show). Heck, with Batman and JL those characters portrayals and voice performances (looking at you Mark Hamills Joker and Kevin Conroy's Batman) are what people compare to. That's not a knock on X-Men, Spidey, or Spectacular - those shows were fantastic as well. But Marvels shows had more misfires than successes. Animated movie wise, it's not even a discussion. Great ones to check out: Batman: Mask of the Phantasm, Batman Beyond: Return of the Joker, Batman: Under The Red Hood, Batman: Bad Blood, Batman: The Killing Joke, Batman: Assault on Arkham, Wonder Woman, Justice League: Doom, Justice League: Crisis on Two-Earths, and Justice League: War.
Comic's wise - it's both. Both companies have an excellent roster of crazy interesting characters. With Marvel, I really enjoy Deadpool, Spiderman, Spiderman 2099, Moon Knight, X-Men (especially the classic Chris Claremont run and Rick Remenders run on Uncanny X-Force), Union Jack, Scarlett Spider, Agent Venom, Captian America, and Spider-Gwen just to name a few. With DC, I love me some Batman, Superman, Geoff Johns run on Green Lantern, Flash, and especially Aquaman was *fantastic*, Justice League, Nightwing, and the pre-New 52 Red Robin run.
While I'm talking comics, gotta recommend both Boom Studios Mighty Morphin Power Rangers and IDW's Teenage Mutant Ninja Turtles. Both are some of my favourite ongoing titles in comics right now.