the biggest difference in my mind is that the Bowyers Edge is made for very precise wood removal. like John said, it is, effectively, a depth controlled cabinet scraper. indispensable for the construction of wooden bows of all varieties, imo. I can't think of any bow I DIDN'T use mine on in the last 15 years. spoke shave is rather useless on any bow with with less than perfectly straight grain. has a tendency to tear up grain, which can be a serious problem. I've only used a spoke shave successfully on a handful of extremely straight grained selfbows.
Bowyers Edge is handy for final tillering where precise wood removal is most important, for cleaning up tool marks left behind from a rasp, for controlled, even wood removal when managing draw weight, for chasing growth rings on back of a selfbow. heck, you can even taper arrows with it.