A tapered neck will ensure more even levels of stress within the neck. A parallel neck will have higher relative stress levels nearer the body than near the nut. Since the relation betweeen stress and strain is constant, a tapered neck will deform more uniformly along its length under the load from the strings; a parallel neck would tend to bend from the heel. So the amount of taper will affect the shape the neck deforms to under the string load.
I knew my 1971 Mech Eng degree would come in useful eventually!