the reason old school games look like crap on modern TVs is due to the fact that old school tube tvs have something called scan lines. if u pay attention to the graphics on a tube tv, ull see these blk lines running across the TV, this is used to smooth out the pixels, think of it as an old school form of anti aliasing
take a look at this video that demonstrates the big difference scan lines made on old school graphics
i actually stumbled across this when playing FF8 on my computer where the graphics sucked donkey balls n found out there were software mods that added the scan lines to make the graphics look better. unfortunately since u r playing on a console, ur only solution would be some kind of hardware device like the one in the youtube video to add scan lines back in