The most obvious difference between soy and whey protein is the source. Soy protein is plant based and is the only plant protein that contains all eight of the essential amino acids. This means that it ranks right up there with animal proteins as far as being a "complete" protein.
Whey protein comes from milk and is the "left-over product" from cheese making. It too is a complete and high quality protein.
Lots of claims are made for each of these proteins. Use your science skills as you sift through all of the information. This paper from The University of Arizona Cooperative Extension may help you separate fact from hype on these protein products:http://ag.arizona.edu/pubs/health/az1383.pdf