Not exactly my turf, but...

... doesn't "perhaps" give you more a sense of accidentality, fatalism, while "maybe" of actual, concrete possibility?
Casual, vs. causal -- if you really want to stretch the envelope?

Well, no, I don't buy it. It's not so much a difference of meanig as a difference that characterizes the speaker: "perhaps" uttered by a careful, older, more pedantic, almost-stuffy speaker (um, that would be me) versus "maybe" uttered by normal people. The degree of possibility is still about 70-30.