I happen to think that glue sticks better to porous feather quill than tape, but I know that tape will and does hold sufficiently. After 20 years of glue-fletching, I gave tape a serious try. Here's what I noticed:
Not all feathers are ground at 90 degrees right angle, base to feather. Whatever the angle, my fletch adhered to the shaft at that angle. Three perfect feathers = a normally spaced and fletched arrow. If a feather base was off-angled (when ground) it would adhere at the off-angle. I had a number of fletched arrows which displayed a flattened 'Y' look when viewed from the nock end. I know the issue was the feather base and not the tape, but the tape has no ability to dry and 'lock in' the feather angle (set by the jig)regardless of base grinding. When using good glue, the feather angle was locked in after 20 minutes and would not move or lean or flatten after the clamp came off. I tried a variety of methods to correct that issue with tape, but it was never as easy as using glue for me.
The other thing I noted was the thickness of the tape, while minimal, was noticeable to me. I could see the tape beneath the feather base, and the end result wasn't as aesthetically nice as the glue produced. I also noticed the elevation of the leading edge of the feather which I definitely didn't like and had to spend time addressing.
In the end, I stayed with glue and can't see an advantage in tape for me. I have a 6-Bitz setup and can fletch pretty fast. I have never lost a fletch from a hunting arrow in any weather or condition. My fletch remain perfectly spaced and angled for the life of the arrow, and I never pay attention to their integrity after the arrow is completed. This is simply me, and the guys who get acceptable results from tape have my admiration.