720 is related to the number of lines on the screen (the resolution).
i or p is related to the refresh mechanism; interlaced (every other line) or progressive.
720i is the lower resolution and refreshes 360 lines per cycle
720p is the lower resolution and refreshes 720 lines pre cycle
1080i is the higher resolution and refreshes 540 lines per cycle
1080p is the higher resolution and refreshes 1080 lines per cycle
As most LCDs don't refresh in the same way that old TVs (CRTs) do, ie there is no raster scan, the difference between i and p is less obvious on LCDs.
Some monitors will accept 1080 signals but will convert them to 720, so be aware of the difference between 'accepts' or 'compatible with' 1080 as opposed to 'actually is' 1080.
I'd therefore go for: 1080p > 1080i > 720p > 720i; however, note the following about the PS3:
http://uk.ps3.ign.com/articles/746/746282p1.html
PS3 Downscales 720p on Incapable TVs
If your TV doesn't support a specific resolution, expect to go low-res.
by Jeremy Dunham
US, November 15, 2006 - As final PlayStation 3 units continue to trickle into more and more hands, additional details about how the system works and what it can and can't do are hitting the web. The latest (rather major) tidbit is how the console treats the upscaling and downscaling of 720p titles on televisions that don't support that resolution -- specifically those that are only 1080i capable.
As it turns out, gamers who own older HD sets that feature only 480i, 480p, and 1080i resolution input capabilities will have to settle for the display quality being downsized as the game boots in its 480p mode rather than upscaling the image from its more desirable 720p mode to the TV's 1080i. We tested this development on older HDTV sets with games designed for 720p but not 1080i -- Resistance: Fall of Man, NHL 2K7, Tiger Woods PGA Tour 07, and Need for Speed Carbon. Sure enough, the system downshifted all four titles to 480p rather than moving up to 1080i. This issue came up with either a digital HD video connection (using an HDMI cord) and an analog HD video connection (using component cables.)
The PlayStation 3's competitor, Microsoft's Xbox 360, does upscale 720p games to 1080i if the HD set supports the latter resolution but not the in-between and commonly-employed 720p resolution.
IGN contacted Sony representatives for comment regarding this feature, but SCEA spokespeople have yet to return our phone calls as we went to press (we'll update this story when they do). It is not known yet if this is purely a software issue or a deeper technical problem and whether or not this lack of upscaling might be resolved on launch PS3 systems in future updates of the hardware via downloadable firmware patches.
For the laymen, 720p is a high-definition format that offers a complete 720-pixel line frame on the screen at 24 to 60 frames per second (progressive), while the 1080i signal is presented as two 540-pixel fields that when displayed back to back look like a complete image (interlaced). The difference being that a 720p picture offers quicker refresh rates while 1080i offers more detail with stationary imagery. The maximum resolution of the PlayStation 3 (and currently the maximum for available HDTV sets) is 1080p. It is thus capable of displaying all major standard-definition and high-definition video outputs wherever HD standards are employed (in PS3 games and Blu-Ray Movies, most commonly), but as has already been reported about PS1/PS2 games and DVD playback, it does not currently upscale any lower resolution images to higher image standards.
