I shoot both parallel or tapered woods; the reduced weight helps when I'm trying to get around the total arrow weight I prefer, choosing Doug Fir most often, which run a bit heavy for my set up.
Suppliers I've spoken with figure the taper might shave a pound or so of spine off the parallel shaft, and tend to mention the slight additional clearance, both of which have been nmentioned here.
As far as actually being able to notice any difference in comparing to parallel shafts, what Orion said goes x2 with me.