I beg the difference between DVD player and DVD player H-Def 1080p up-conversion. Which one should I keep?

I got one DVD player and the other DVD player H-Definition 1080p up-conversion. Both of them seem to play the regular DVDs. I have both tube TV and LCD flat panel HDTV. The regular DVD says progressive scan. But the other says it has such function, and only works when it is turned on. Each time it is turned on the regular TV, it will be turned off. I just wonder if the regular DVD player works in reinforced manner even if the TV is incompatible with progressive scan. How does one know if the TV is compatbile with the progressive scan?