There are actually a couple of different variables at play here.
First, if you have a 1080P screen and you're playing 720P material, the material actually gets stretched to fit the 1080P dimensions. Exactly how that's done plays a large roll in how the quality of the image is preserved. Basically, the TV inserts rows and columns of pixels and does its best to blend the actual pixels from either side to make it as seamless as possible. But different algorithms are employed by different manufacturers and the ability to do this is also sometimes dependent on the hardware available so there can be some difference in the end result from device to device. This is done by your TV when you're bringing in a signal from an OTA antenna, and depending on your components, it can be done by either your cable/satellite box OR your TV if you're getting cable/satellite depending on how you have things set up.
For distance, THX says to take your screen size and divide it by 0.84. For a 60 inch screen, that would be right about 6ft away.
But THX is trying to maximize your field of view (filling up your focus with the picture) more than worrying about how sharp the image appears.
The following chart indicates how far away the average person with 20/20 vision can sit before noticing the difference between 720P/1080P (and other resolutions). It would seem to indicate that 12 ft is where you can tell the full benefits of 720P. But remember that you'd be watching a 720P signal that has been manipulated to actually be a 1080P image with (hopefully intelligent) filler. Technically, a 720P screen would probably look better displaying a 720P signal than a 1080P screen displaying a 720P signal that has been "converted". The quality of the image now depends a great deal on the quality of the conversion done to it.
Try this on your TV via Chromecast or something and see how it works.
Carlton Bale has put some great material out there to help people understand this stuff.