It's not easy to answer to this question, but as far as I know:
Shade is very popular because it's available as a japanese product, and it have a lot of books available, and all kind of resources.
It have a very strong history, it's now an "old" software, and as you can imagine, a long history in the user minds.
And it is a very stable product!
Doing a comparaison between Carrara&Hex with Shade isn't easy. They way you use the software isn't th same at all. Shade is almost all spline based, far away of what splines can do! It have several render engines, included the well known Callisto (in Japan) and have a beautifull radiosity engine.
The polygonal modeling is the same as Carrara STD I think, but I prefer modeling in Hex or Amapi (well, I have a specific background for that
I'll post later some links from the japanese galeries, some stuff are amazing!