I find both terms a bit awkward, neither completely satisfactory in a denotative sense (they don't hold a candle to "Bayesian" in that regard). I think rationalist comes off as a bit more hubristic. Naming ourselves does draw artificial lines, implying that we're "more of that" than others. So when we call ourselves rationalists, we imply that the other party is irrational. When we call ourselves evidentialists, we imply that the other party isn't paying enough attention to evidence. The latter seems less immediately offensive, and I would expect a less defensive reaction in turn.