amok: There are crossover between the 3 (for example Gog do not do alphas and betas, while Desura and HS does), but purely mechanically, I do feel that GoG and HS are more similar and fill a more common niche.
I don't feel that way.
For me it's like that:
both Desura and HS are mainly for Indie Games, and for GOG it's just the part of their market
both Desura and HS are partially Steam-codes store, while GOG is drm free only
both Desura and probably HS (we don't know yet, but I think we can assume that basing on HS widgets) are open for almost all kind of games (like GG, but less), while GOG tries to select titles they sell
and also, I think you are right about modding community, but I never saw that as a major selling point for Desura; it was nice idea, but something didn't work out.
On the other hand, GOG has very good community too, contrary to those stores that are "just stores", and for now it may look like HS will be just store.