In my research for shopping for my own TV, I've discovered yet another wrinkle...
As it has been pointed out, the HDTV resolution is much higher than most of the current sources. However the TVs vary greatly in how well they "upconvert", improve or clean up, the signal from non HDTV sources. The specs don't tell the whole story as some claim upconversion technology (that varies greatly in terms of how well it works), or they may use various noise filtering or other techniques.
In the end, find a good on-line review for your tentative TV choice, and the better reviews will tell you what kind of a job it does displaying old TV channels (or video tapes, DVD's, etc).
I hope that helps!