I beg to differ.
The DPI difference between the two is huge. For a 100" TV with 1080P, the DPI is around 210. 7680x4320 is a huge resolution, if that was on a 100" TV the DPI would be about 3300.
I would definitely be able to notice that difference.
Two things you should look into:
1> Resolving power of the eye (past a certain point at a certain distance, your eyes can't tell the difference in detail). For most people, the differences are negligible between 720P and 1080P at average screen sizes and viewing distances because the eye cannot resolve more than 720P beyond 6 feet or so from an average HDTV.
2> He was comparing a theater screen (say 100 feet) to a 100 INCH tv screen versus resolution. So the comparison is 4320 lines on 100 foot versus 1080 lines on a 100" screen. I would imagine the 100" screen will look better at a normal viewing distance for each size screen (4320 lines / (100 ft *12 inches per foot)) = 3.6 versus (1080 lines /100 inches) = 108
I have a 93" screen with a 720P projector and sit at 8 feet. I should be able to see a small improvement at that distance with 1080P, but it would be small and that assumes the source material is actually utilizing that extra resolution (many movies do not). But arguing about 720P versus 1080P on a 32" tv is moot unless you're sitting less than 3 feet from it.