Depends on the fining agent, I believe. Some strip more out than others, I am told, with filtering stripping the most. I think gelatin and Biofine Clear work good and don't seem to drop the flavor significantly. The Biofine is silicic acid or something like that, so it pulls out the chill haze causing proteins, too, so maybe it affects the taste more than gelatin. ILike gelatin because it works in a couple days and I can put it into the serving keg and not have to rack further or remember to add it prior to racking...YMMV, of course.

+1. Gelatin drops hop aroma and flavor a small amount in dry hopped beers IMO. Hop oils bind to yeast, so since gelatin is so effective at dropping out yeast, it drops a bit of the dry hop character with it. Not dramatically, and I account for it by increasing dry hop amounts slightly when I use gelatin on an IPA.