Hmm, I'm more used to the movies honestly so I'll have my favourite MCU/DC Movie characters and then see if that changes.
DC - Batman...specifically The Dark Knight's Batman
MCU - Hmm, either Thor, Captain America or The Hulk/Bruce Banner.
DC - Honestly, I'd have to say Batman but I know that this is based off his recent popularity and the fact that he gets more coverage, movies (animated) and so on. I'd probably say Green Lantern otherwise, I really love the idea of the GLC, and they just got the short end of the stick because of the Green Lantern movie.
Marvel - Honestly, I've got no idea, I can't really say that I have a favourite. I generally like DC more than Marvel with the exception of the recent movies so honestly... yeah I don't really have a favourite because I've never read a Marvel Comic or anything other than the MCU.