I just looked both up:

Parochial seems to have the first meaning of "of or concerning a parish."

Both seem to share the meaning of being local, narrow, restricted in scope, limited....

Provincialism has the above as its primary meaning; as a secondary meaning it has "allegiance to or concern for one's province rather than one's country."

So perhaps the latter has a slightly broader scope of narrow-mindedness than the former...?! (assuming that provinces tend to be larger than parishes)

instant edit: nearly forgot to add that "parochial," to me, always seems to have a more patronising air than "provincial." The former is arrogantly ignorant/narrow; the latter is innocently so. Summink like that.