I'm not sure the distinction between axioms and definitions quite gets to the heart of it. If by "definition," you mean stipulation, as in the sort of fiction that's meant to be more convenient than reality-based, then I think the key question is whether analytic or literary philosophers are more likely to be up-front about that fictive side of their reflections.

There are also rationalists and empiricists in math, I believe, although the Platonists may outnumber the empiricists.