When it comes to which one overall I'm more of a DC fan, but for modern comics I have to go with Marvel. I'm reading more Marvel books right now, and their events, while usually frustrating, don't tend to screw up as many books as DC's. It feels like more writers are allowed to actually write their books without having to worry about being derailed every other month (not that Marvel doesn't do that sometimes, but it generally doesn't do it as much, and when they do it usually only screws with the really big books like Avengers).
Also, Marvel is 1000% the winner in the diversity department, both in the styles of the books and the actual diversity of the characters. DC books right now, possibly as a side effect of constantly having to bow down to Scott Snyder's semi-monthly shit events, almost all have dark tones and have similar issues with inconsistent writing coming from never being allowed to have a status quo. Marvel on the other hand has everything from Immortal Hulk to Thor to Guardians of the Galaxy and more being extremely different from each other and offering different things (horror, cosmic adventure, comedy, etc).
Character wise, DC seems to actively fuck with everything people start to like that doesn't fit in with that months grand plan, and its track record with character diversity is getting pretty grim (see the recent "Harley Quinn and Poison Ivy are totally not a romantic couple" thing that has gotten some people upset in the last few weeks). Not to mention a bunch of unrelated characters getting "infected" with the dark universe and having their books ruined because of it (Supergirl becoming an evil edgelord completely ruined that book).
Marvel, on the other hand, just explicitly confirmed that Mystique is married to Destiny, which is just a recent example of Marvel, even when it was totally under Ike Perlmutter and his minions control, allowing more diverse content then Dan Didio allows. Marvel also just has more variety in which characters get to have books, with Ms. marvel, Black Panther, Miles Morales, etc all doing well while DC does stuff like canceling its excellent Green Lantern comic starring POC Lanterns so that the blandest white man in the galaxy can be the star of the sole GL book. To be completely fair to DC, Marvel in the last few years has also made a holocaust survivor character into basically a nazi and hired an editor who wrote comics pretending to be an asian woman to a high up position, but on the other hand that was under Permutter who is now not in control of the comics, so hopefully shit like that stops happening.
Overall, as much as I love Marvel I'll always love DC's characters a bit more, but the last decade has been pretty bad for DC, and at this point even the good stuff that came out of DC Rebirth has pretty much been eliminated by management that really just wants dark, grim, edgy stuff to sell even it is obvious that people want more variety then they'll give.