I think they are pretty similar, the biggest difference being the free breakfast, but no other food options, at the Hampton and the cooked to order (but you need to pay for it unless you have status breakfast, also some dinner options and a bar) at HGI. Honestly, I would go by cost, whatever is cheaper assuming location was the same/similar. Of course there could be certain places where one specific property is better than another.

I go regularly for work to a town where there is an HGI and Hampton nearly across the street from one another and simply pick whichever is cheaper.