I think I'd be of the persuasion that says no particular theory should be considered "foundational" to mathematics. In my opinion, they are just different faces of the same multifaceted coin (maybe there's a theorem involving a coin with more than two sides in there somewhere?).

Really, I can't say, though. I'd certainly be interested to know what you think. It's not a topic I've previously put a great deal of thought into, so if you have insight... well, please share!