I've shot both for a lot of years and can't really decipher much difference in the way they fly, though theoretically, the tapered shafts recover from paradox a bit more quicky. Also, because there should be somewhat less flex in the shaft on impact, they should penetrate better. However, I haven't noticed a difference in penetration on deer size game, probably because most times, I get passthroughs. I do my own tapering and tend to shoot tapered shafts more now.
Depending on the diameter shaft, tapering the nock end will reduce the weight of a 11/32 shaft by about 20 grains. Likewise, footing it will add about 20 grains to the front. More for 23/64 shafts. So, you can get slightly higher FOC by tapering, slightly more overall weight with a parallel shaft. Another way to add weight to the shaft is to soak it in Watco or some other oil. That generally adds about 50 grains to 11/32 shafts. Good luck.