In Hilton's ranking of their various brands, I think Hamptons are definitely lower on the scale. However, when I've traveled to areas where there are both HGI and Hamptons, the pricing doesn't necessarily track.
The HGI 'restaurant' also means you get cooked-to-order eggs for breakfast versus what they put out at the Hampton each day.
Also, IIRC, there's a Keurig machine in HGI rooms versus a filter packet type thing in the Hamptons.