As far as I know all current generation HD disc players can be set to output in all standard HD formats as well as SD formats. So, you can set the player to match your display perfectly, or let the display scale the 1080p/24 source to your liking.
1080i, 720p, 480p, and 480i are all standard output resolutions on HD disc players. Since the source is 1080p/24 for most film based material, some scaling/processing always needs to go on to get to these resolutions. Therefore, the question becomes where does the best processing take place?
I would think that it would best occur in the player as many HD displays do not properly handle 1080i material for deinterlacing. So, feeding 720p is likely the best way to go. Unless the player does a poor job with that 1080p/24 or is it 1080i -> 720p conversion as well.
As for actual on screen quality: It will be better than DVD, but not necessarily by a lot. DVD looks pretty darn good right now and HD discs are considerably better, but it only matters if your screen is big enough and you are sitting close enough... or your old DVD player really sucks.