Is there a schsim between classical logic and categorical logic?

Question

I've been trying to learn a little bit more about the foundations of mathematics, and it has strike me that there seems to be two competing points of view about what the foundations should be. While classical logic seems to focus on a set theory like ZFC or an extension of it, in categorical logic you will use something like ETCS. Are developments of the two points of view mostly parallel? Is there a dominant point of view at the moment? Is there some kind of schism between proponents of the two points of view? Or will they mostly go to the same logic conferences and hang around together?