Which 500 mm camera lens is better and why - refractive or reflective?

I have finally switched, kicking and screaming, from Canon FD lenses to EOS. I had a nice collection of FD but they are all manual and don’t work all that well through an adapter so I want to get a new telephoto. Not one of those white ones with four-figure prices but one I can afford as a soon-to-be-retiree. I have FD lenses in 300mm and in 500mm which are refractive and reflective, respectively. So comparing them isn’t exactly apples to apples. I just can’t say for sure which gives me the better quality photos.