I'm a Batman fan through-and-through, but I have to say that the Marvel franchise is my absolute favorite between Marvel and DC. DC let me (and I presume lots of people) down in how they approached their movies by dropping us into a shared universe with no back story (movie wise, not talking comics or cartoons etc) in where we generally couldn't care less what happens to the character, as opposed to building character relationships over one or more movies. I do have to say, though, that while Justice League and Batman v Superman were not the highest par, Aquaman and Wonder Woman were of Marvel-like quality and I got behind them. I hope the new Joker movie is going to be just as awesome.
I really like "Watchmen" and "V for Vendetta" I enjoy most DC content, however I've never been a huge fan of Superman because he's such a Mary Sue.
I have yet to see all of the modern content of either of the comic titans live-action movies, but in general I feel like Marvel has been doing better on their movies and it is difficult for me to place exactly why. It might simply be the lack of cohesion to their cinematic multi-verse as Andrew stated.
However, DC does has been running several live shows which have been pretty fantastic: Arrow, the Flash, Supergirl, Black Lightning, etc; and I do feel that these show have been of at least comparable quality to Marvel's television series. If the shows don't fall flat, then why do the movies?
I enjoy both Marvel and DC content but, as far as the movies I've seen go, it has been a while since DC has really wowed me.