My opinion comes from a comic book geek in self-imposed exile from the big two. This is mostly due to lack of funds and frustration between the companies failing to evolve in some meaningful way imo.
I like Marvel better than DC, but only by a small margin.
Marvel has great characters. Each one, whether they are demigods or average people, have feet of clay. DC has some great characters too but they seem too perfect at times. This is why Grant Morrison referred to them as Olympic gods during his JLA run. A team like the Avengers is more like a group of friends and family working together for a common goal. They bicker and disagree and irritate one another but, at the end of the day, they put aside the differences to focus on the threat at hand. Yeah, DC has relationships like that (I.E. the JLI era or Wally West Flash and Kyle Rayner Green Lantern or Ollie and Hal for that matter) but that is due to the writers catching up to what Marvel already covered.
Story wise, I'd say both have their best runs and storylines. I can think of many Marvel sagas that stand out as the best (see Ultron Unleashed, Under Siege, and the Kree/Skrull War from the Avengers comics) and its had some classic writer runs (Chris Claremont and Peter David to name a few) but DC isn't a slouch in those departments either (Grant Morrison's JLA run, James Robinson's Starman, and Batman's Long Halloween for example). I'm sure many folks here can offer their favorite DC or Marvel writer era or comic story line or series to recommend to anyone.
With all this said, I'm at a point in life where I've grown tired of comics from the big two. First off, trying to keep up with multiple series with price covers of three dollars or higher while slogging through highs and lows of runs tends to make the hobby less enjoyable.
After DC pulled their New 52 line, I left that company behind. Tossing out their history to bring in new readers is a flawed idea. The company has broken their continuity so many times, its hard for any fan to keep up with what is considered cannon or not (a number of MovieBob's Big Picture episodes can attest for that). Marvel still has its continuity in place and is trying to bring in readers but with multiple titles of a certain team plus dragging us into one event crossover after another is not winning them any popularity contests. Plus both are guilty of over-saturation and price gouging but that is just how I see it. I could make an entire message thread of my beefs with Marvel and DC recent actions.
Lately, I'm getting back into TPB's and mangas. I'm currently caught up on Naruto and I'm now playing catch-up with One Piece. Meanwhile, I'm looking into books I never tried before until recently. I'm currently into Volume 6 of Eric Powell's The Goon (Chinatown alone cemented my vote for The Goon to be my all time favorite comic book character) and have just dipped my toes into Darwyne Cook's Spirit run (like to get into the original run by Eisner but that's gonna take some serious cash).
While I miss collecting Marvel and DC a bit, they have a long way to go before it can win this fanboy back to the comic book shop.