DTV Standards
The simplified chart below outlines the various Advanced Television Systems Committee digital standards adopted in the United States.
Although there are numerous factors involved in evaluating technical quality, from a purely technical standpoint the greater number of scan lines on the screen at any one time the clearer the picture will be. In addition, the progressive approach to scanning will result in a higher technical quality than the interlaced approach.
It should be noted that the HDTV standard of 1,080 lines shown below is the same as previously discussed the 1,125-line HDTV standard. The difference centers on the total lines broadcast (1,125) vs. the active visible lines (1,080). As in SDTV, many of the lines that are broadcast do not end up being displayed on the TV screen.
Active Lines Per Picture Pixels Per Line Aspect Ratio Frame Rate Scanning
Approach
1080 1920 16:9 24, 30, and 60 Progressive
1080 1920 16:9 24, 30, and 60 Interlaced
720 1280 16:9 24, 30, and 60 Progressive
720 704 16:9 24, 30, and 60 Interlaced
480 640 4:3, 16:9 24, 30, and 60 Progressive
480 640 4:3 24, 30, and 60 Interlaced
To simplify things some minor formats are not listed.

720p vs. 1080i
There are ongoing debates on whether 1080i or 720p is better for HDTV.
Those who say 1080i is better say that 2,073,600 pixels for HDTV are "clearly" superior to the 921,600 used in 720p.The more lines, the more picture detail.
But, again, there's the issue of the number of lines that appear at one time. Since 720 is progressive and 1080i isn't. This means that the 720 standard ends up being better for tracking action, plus you won't see any "jaggies" or motion artifacts with 720p.
The newest tuners should be able to convert any of these standards into a TV receiver display. At the same time, some tuners/receivers display one standard better than another.

The 24p Standard
So-called e-cinema or digital cinema has moving to the 24p standard (24 frames per second, progressive scan). Those who are after the "film look" prefer 24p, because the progressive approach results in fewer artifacts (aberrations) and because the 24 fps video rate is the same as film.
When projected, and with the proper equipment and electronic setup, both 24p and full HDTV become almost indistinguishable from film. If there is any "fault" with digital video it's that seems "too sharp and clear" compared to film.
Of course, I guess we can all get used to better quality if we really have to!