[One (M7) General] BarryH_GEG:
This is from the article I linked. I've highlighted some relevant things. We didn't talk about rescaling which means a 720P video on a 1080P display will look worse because it's being upscaled. So to get the benefit of the higher resolution people need to use 1080P content. And if they do that their going to run out of storage space. And that brings us to a whole different conversation. ;)

Whether there's a difference or not doesn't really matter; whether the One or another new high-end phone we'll all end up with 1080P displays any way because it's the new "black." But hopefully for 720P phone owners this discussion minimizes some of their "display envy" so they won't feel that burning need to replace a perfectly competent device. For OG One X owners they'd actually be making some trade-offs.

"When it comes to 1080p on a smartphone, he admits that it might not matter for the most casual users. "For some people,

it is possible to tell the difference if we were to sit down and study a [1080p] display and a [720p] display, side-by-side

," he said in a phone interview with Ars. "

If you’re really a fanatic and you study images, or you have some professional applications and you’re really into displays, then it may make a visual difference for you

."

For most people, though, it won't matter.

Photos are inherently fuzzy

, so it won’t matter whether they’re viewed on a 1920×1080 or 1280×720 smartphone display; you’ll still see their imperfections. "

Even the tiniest image detail in a photograph is always spread over more than one pixel

," Dr. Soneira explained in a follow-up e-mail. "

The image detail is never perfectly aligned with the pixel structure of the display

."

Videos are even worse: not only are they fuzzy like photographs

, but the pictures are constantly moving.

Even if the images were sharp, the human brain couldn’t zero in on content that’s appearing for only a fraction of a second on such a small display

. "For ordinary viewing of videos, 1920×1080 is really not going to make a visual difference," adds Dr. Soneira.

Where a 1080p smartphone display could really make an impact is with computer-generated content—that is, the user interface, buttons, and text. "

Only computer-generated images make full use of the pixel resolution of the display

," says Dr. Soneira. "For graphics and text, maybe you want that kind of sharpness." Like desktop computers, smartphone displays can also utilize sub-pixel rendering, which helps improve the visual sharpness of computer-generated graphics.

A 1080p display might also be useful for simply viewing 1920×1080 content

and not worrying about scaling. "

Every time you rescale content that’s scaled for some other resolution, it’s not going to look as good

. So there’s an advantage to living with 1920×1080 even if your eye can’t appreciate the fine details, because you don’t have the rescaling artifacts," he says." ​

Here's the author's bio. I'd guess he's more credible than the 20-something with no formal education in display technology that did Gizmodo's review.

Dr. Raymond Soneira - Founder, President and CEO of DisplayMate Technologies Corporation

Dr. Soneira's background covers a wide spectrum of internationally recognized leading edge research in electronics, optics, applied mathematics, theoretical and experimental physics. For example: he has designed color television broadcast equipment for the CBS Television Network, built a computer mathematical model of a television system for optimizing the camera to receiver performance and accuracy of the optics and electronics for CBS, a leader of a team at Bell Labs Research that built intelligent autonomous mobile robots, designed an all-electronic 360 degree viewing angle imaging laser range finder using the parallax principle, did the mathematical foundation of the fine guidance system for the Hubble Space Telescope, built the accepted standard model of the Milky Way Galaxy (which is named after him), built theoretical high redshift cosmological and stellar models for the Hubble Space Telescope, has done fundamental work on the analysis of clustering and super-clustering of galaxies, plus work in Relativity and nuclear physics.​