What Is The Difference Between 720p And 1080p In Regards To A Hi Def Tv.?

1080p is a higher resolution than 720p. That’s really the only difference between them.
Whether 1080p is worth the extra price, that’s debateable….
First, the only source for true 1080p material is currently HD-DVD or Blu-Ray discs. Almost all TV channels that are in HD are only using 720p, with a very very few using 1080i. Even the newest video game consoles, the PS3 and Xbox 360, really only do 720p since that’s usually what the games support. There are a few that may do 1080i, and one or two that do 1080p, but they’re going to be in the vast minority.
Second, on smaller screens (under 40″) you probably won’t be able to detect the difference between 720p and 1080p even if you have a 1080p source (e.g. blu-ray movie) connected. Even on larger screens, depending on how far back you sit from your TV, you may still not really notice a big difference.
As for TV recommendations, I really like my 60″ Sony rear-projection set. This TV combines the benefits of a LCD TV with the lower cost of a rear-projector. The picture is just as good as a normal LCD screen, but only costs a fraction of what a normal LCD screen of that size would cost. Unfortunately, Sony is discontinuing their rear projector line this year to go 100% LCD, so this will be your last chance to get such a set (and maybe even on sale!)
Otherwise, I really like Sharp’s Aquos sets for smaller screens, but they’re relatively expensive. If you want a bit more of a budget line, check out Olevia, which still has a very good picture, but isn’t as expensive as those other big brands.

Typically it’s in the screen size, anything 40 inches and over will get the 1080i and 720 is for 36 inches and less. Anything under 40 inches wont be able to properly display the screen.

1080p is not a broadcast format.
If you watch HDTV from cable, off-the-air, or from satellite the stations are either 720p at 60 frames per second or 1080i at 30 frames per second.
1080p is supported only by high def DVD players or advanced game consoles like the Play Station 3.
Stations like ABC, Fox, and ESPN broadcast in 720p and have a higher framerate so sports action appears smoother.
Stations like DiscoverHD broadcast in 1080i because the resolution is better and panned camera shots look fantastic.
Anyway, if you have a 50″ HDTV set and sit more than 10 feet away, you can’t tell the difference between 1080 and 720 anyway. There are charts on line that show the benefit of the higher resolutions up closer for various screen sizes. It’s quite interesting.
If you’re gonna watch the game and not sit up close to the TV go for the 720p set. If you are going to watch movies go for the 1080p set. HD DVDs are encoded at 1080p. If go for the movie route and can affort the extra features, just make sure you go for the sets that can accept and play 24 frames per second content (like movies) as well as 30 frames or 60 frames per second (like TV video).

If you are purchasing it to watch HDTV save some money and get a 720p set it can display up to 720 vertical scan lines in a progressive manner, so you can watch all the transmitted formats in the USA including 1080i, 720p, 480i, and DVD at 480p. 1080p is a higher progressive scan of 1080 vertical lines and in the USA the ATSC standard doesn’t include this resolution, also HD cable and HD satellite do not support 1080p. If you want to watch 1080p you need a Blue-Ray player or HD-DVD player or a PS3 (Blue-Ray built in) so if you don’t plan on one of these in the near future get a 720p HDTV, keep in mind the Blue-Ray, PS3 and HD-DVD will work with 720p just not at there max setting of 1080p. As for 1080i it draws 540 odd then 540 even then interlaces them to trick the eye into seeing 1080 lines. So a true 720p drawing all 720 lines progressively (at once) is actually better.
For most HDTV viewers I recommend 720p. Samsung and Panasonic are top rated, Sony and LG are also good. If you want a lower end and less expensive LCD HDTV look at Vizio and Olevia.