With both dish's being 6', the gain should be close to the same for both. The more important factor may be the F/D ratio, as it will determine the adjacent satellite rejection.
I'm curious relative to what you base this statement on?
I think I know where you're coming from, ie from an optical standpoint you intuitively expect to get more resolution as you go to higher F/D ratios, and longer focal lengths give you more magnification to resolve close together objects, etc. However every equation I've seen for resolution or beam width of a satellite dish generally say that resolution is completely dependent upon gain, and that gain is pretty much completely dependent on dish size, etc. If there are equations out there that involve F/D ratio, I'd appreciate a link.
From experience, ignoring any equations, I really had much better results in this respect, with a relatively high F/D Sami dish, than I currently have with a LOW F/D Orbitron dish. (I really miss my Sami, but it stayed with my old house.)
However I also think that the high F/D Sami also had more gain, despite being the same size as the Orbitron, mainly because the feed had a better view of the outside edges of the dish, which are pretty much wasted space on the Orbitron.
But anyway, are you aware of any web page with theoretical discussion with equations, that involve F/D with respect to resolution/beam width? Just curious.
EDIT: another aspect of this, is that offset dishes generally have very HIGH F/D ratios. However the dish is a small section of the complete parabaloid, and if the F/D ratio were calculated based on th entire parabaloid, the F/D ratio would be much smaller. Ie this is somewhat similar to stopping down the iris on a camera, or using one of those lunar covers to a telescope to get a clearer image when you don't need the light gathering from the entire mirror.