Neither. All the best stuff is creator-owned these days, if you ask me. Image and Dark Horse are the biggest and best "third party candidates," but Boom and Dynamite have some good stuff, too.
Honestly, find an author that you like and follow them, not the characters. Mignola, Lemire, Hickman, Faction or Gillen can write absolutely anything and make it compelling, and there are a ton of other interesting, unique authors out there these days.
If you want specific series or arcs, HMU with a few examples of what you like and I'm sure I can throw out a few suggestions (and if I can't, someone else can)
I do read mostly the indies because it's just too much work for too little payoff to try to follow a mainstream series, and I'm way more into sci fi & fantasy (and fantastical not realistic horror) than superhero stuff. I wait for each season to be collected into a paperback then get it. There is so much out there.
I like superhero, strongman type comics that have some complexity of character (not simply smash the problem away) Thor, My Hero Academia: Deku and Allmight, Hyperion, Superman, Silver Surfer.
Lemire and Ellis's runs in Moon Knight are amazing.
You also might really like Black Hammer, which is like a deconstruction/reimagining of the Silver Age Justice League (I think it's Dark Horse, but it might be Vertigo). In general, I tend to like more high brow/pretentious stuff and the art, the characters, and the plot are all spectacular.
Edit: plus Hellboy, obviously. Mignola's art and love for pulpy, over-the-top monsters and plots are just phenomenal, IMHO. Nothing like Lovecraftian horrors and world-shattering battles to make for great comics
Edit 2: you mentioned Silver Surfer, so I'm also assuming you've already read Hickman's run on Fantastic Four and FF. If not, start there. It's one of my favorite Marvel runs of all time
I think they do better at different things. I think DC does better at graphic novels and self-contained stories, but Marvel does better at ongoing stories and handling continuity (or handwaving it away).
Marvel: s (NY, ) mixed in with fake locales (Genosha, A events (9/11 has made several appearances, WWII is canon), legit in-universe stakes and motivation, lots of difficult or morally grey choices. Good reading, they make you think.
DC: fake cities (i.e., Metropolis, Gotham); never have seen a historical event (feel free to enlighten me if you would); stakes seem to be damage to infrastructure and property — maybe a hero or two will get hurt (except for that one time they put a lady in a refrigerator as motivation — that was not cool); good guys are clearly good, bad guys are clearly bad.
Every time I've tried to get into Marvel I'd find out that I had to read like 17 different crossovers just to be able to start in on a current issue. It became the same with their movies where everything is interwoven together. Which can be great if you watched it from the get go, but jumping in halfway through could be daunting.
While DC does do crossover events they are usually much shorter and self contained. Although when they started all these huge crossovers with the New 52 and the rebirth, is when I stopped buying the monthly editions. Now I just wait for the stories to be packaged into graphic novels or collections.
DC because they have some more imaginative stories under smaller labels. Looking at my shelf, most of mine are Image Comics, but Vertigo is (was?) a DC label and some of my favorite stories are in those books.