HDTV's can't display SD resolutions natively. They have to deinterlace and re-scale them before they can actually display them. HDTV owners have complained for years now about how badly this often turns out. Video scaling in HDTV's is often rudimentary, yielding disappointing results. In other cases, cable and satellite receivers will handle this video processing, again often with disappointing results. This is of course compounded by scale: most HDTV owners are looking at 42" or larger screens, whereas most SDTV's are going to be less than 36" - the extra screen size just highlights those weaknesses in the source.

If you feed a 1080i source to a 1080p-native display, the TV will deinterlace that 1080i (interlaced) signal to 1080p (progressive). If you feed it a 720p source, it will scale the signal from 720p to 1080p. This is assuming that the display is truly 1080p (which early "1080p" displays weren't exactly).

I'll leave it to others who have gotten some first-hand experience with 1080p displays to say how it compares to 720p and 1080i displays...