720p vs 1080p is a non-issue until you exceed 65 inches and enter the realm of projectors then the resolution really matters. The human eye can't distinguish the difference at close viewing, small screen size.
I can certainly see the difference between my 26" 720p and my 32" 1080p.
It all comes down to how far are you from the display.
If the 32" was 720p I would not be able to use it. Don't forget that computers can use the extra resolution.
If you're using the screen in a computer desk, then, IMO, there's no questioning wether to buy a 720p or a 1080p, unless you've got bad vision. In the desk, the real question is if the 1080 is enough
The GPU point is a good one, but for me it's more about the TV resolution compatibility. A TV screen has a limited number of resolution modes, it's very likely you fire up a game and it sets a resolution not supported by your TV. You'll just get a "resolution not supported" message on the screen.
With my 8800GTS I had to use the HDMI connection and install a nvidia fix that enables the upscalling functions on the nvidia panel. This way, if a game starts at an unsupported resolution it can be streched (with incorrect/correct aspect ratio or have black margins) and you can change the resolution to a higher one.