Freespace 2 works well in my Win 8 (which is mostly a reskinned and tuned Win 7). I admit is the 32 bit campy version, guess there may be trouble in 64 bit.
I may try my German CD version from around 2004. If this works, the GOG version should do, too.
Quite often the problem is somewhere else (e.g. drivers, HW features etc.) than the OS itself.
Hm, quite old games for Windows can be problematic in graphics, but why should there be a difference between NVidia and ATI/AMD? Unless it’s a Voodoo special edition, I don’t see the point.
I had more problems with Windows7 itself, e.g. playing Starcraft. This is quite impossible playing fullscreen without colouring issues, unless you use Windows XP. And this is not the only game with this special problem. Only patching could help, and I think, GOG has access to the source code, if it helps.