As to the TDKR vs Avengers debate, I think Avengers better accomplishes what it sets out to do, but what it sets out to do isn't very compelling for me. It's a big, dumb action film with the faintest hint of any depth at all. It doesn't explore any themes, has no character arcs, and the character motivations are wafer thin, and completely rely on the previous films.
TDKR is, for me, the better film. It's more ambitious, attemps to explore interesting themes, and the characters have arcs that are built and created within the events of the movie.