A 7870 should give you excellent performance at max or near max settings at a resolution of 720p. As for image quality, it just comes down to the quality of that particular television, the same as it would if you were watching movies or hooking up an Xbox.
The TVs refresh rate is 60hz, so you won't be able to see framerates any faster than 60 fps. Not that your eye could distinguish them any faster than that anyways.
I could see you maybe referring to the dot pitch, but picture quality depends more on color balance, contrast levels, brightness, viewing angles, and response times. Screen size wouldn't even be one of the things I listed in regards to picture quality.