In the US most (not all) HR lounges have really terrible breakfast (it's the same standard stuff at most of them). This is unfortunately true even at some really nice HRs.

I think GHs tend to be bigger and more upscale in general (which does not necessarily equate to better). GH tends to be my favorite brand in general.

Also I think that when you go to resort-type hotels the difference becomes harder to notice. There are some very nice HR resorts. But in urban areas with both GH and HR, the GHs tend to be nicer (the only exception that I can think of off the top of my head is San Francisco. The HR on market is also one of the exceptions to the rule of terrible food in HR lounges; it's great there)