I understand that you like to over analyze these things with your science and math, but what I'm saying is not that complicated. From my personal experience, I can see a huge quality difference between the Nexus 5 and Droid Razr HD. For anyone to make a statement before seeing and experiencing themselves seems foolish to me now that I have seen it for myself. Having said that, I'm not saying that we need infinite amount of resolution on our phones. I assume there actually is a limit to where we will no longer notice a difference. It could be 1080p on a 5" display, it could be 4k on a 4" display, all I can say is "don't knock it before you try it."
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I appreciate what you are saying as well, and yes...I can be a bit over the top (sorry).
There's no disputing the information you are saying (and I certainly didn't intend for it to sound that way if it did). If it looks better to the eye...it is. All I am clarifying is that the difference you or others see may not be simply due to the higher pixel count. There are many other factors in displays that blend to result in either a good or not so good user experience. Contrast ratio (black levels), color saturation, dynamic range of color (16 bit, 32 bit, 48 bit), refresh rate (or frame rate), brightness, pixel arrangement (Pentile versus standard rows, versus any hybrid thereof), type of display (whether it be LED, LCD, OLED, etc.), type of glass used, coatings, etc.
It's almost the same as the rush to push the megapixel race in digital cameras. Nikon has proven so many times over that more pixels doesn't directly translate to better images. They've taken their engineering prowess and placed it where it does the most good. The best possible optics, when all other things considered are the first and most important parts of any image capture, and so the quality of the glass, the refraction index (how much light bends or diverts at point of entry or exit in the glass), how clear it is (which translates to allowing more light through), what coatings are applied which can either increase visibility or reduce glare, etc., all contribute to the amount and focus of light that reaches the image sensor. There are also lots that can be done on the back end, after the sensor which will have a huge impact on the final image. The software algorithms used to take that numerical data and convert it into light and colors can be very good or very poor, or somewhere in between. Obviously the quality of the sensor plays a role, and there is good reason for being in the 5-10 mp range for enlargements, but it's one factor of a plethora of factors that go into the mix.
So what I am saying is that when it all comes down to it, more pixel count
may have an impact, but as you mentioned there is a point where the number of pixels per inch is past the limit of human perception at a specific distance. One thing is for sure...more pixels means more power and more data, which means more battery consumption and greater need for processing and graphic power, so with two identical devices side by side, one with a 1080p display and the other with a 720p display - all other things being equal the 1080p display device will be able to produce less frames per second than the 720p device. In that case, the 720p device can actually look better when watching a video with a higher frame-rate than the 1080p device is able to keep up with.
The only way to know for sure if one display is better for you than another is to see them both, in person, displaying the same images, and side by side. Nobody but you can tell you what your eyes can see and your brain can process, so nothing said in these posts is going to be 100% right for everyone, except that once the maximum resolution the eye can discern has been exceeded (again, all other things being equal), there is no added benefit to those higher pixel counts, and in fact there may be good reason to steer clear of them.
I have a Droid MAXX and had a Samsung Galaxy S4. I can say definitively that I am not in the least disappointed with the "quality of the image" on the MAXX, with its 720p screen at 294 PPI versus the 1080p screen at 442 PPI on the S4. Also the MAXX has a considerably slower processor with less cores, yet it is every bit as fast as the S4 was. Finally, the MAXX is only slightly larger than the S4 (length and thickness), but with the same screen size it has nearly twice the battery life per charge. I would sooner sacrifice the resolution of 442 PPI at 5" - effectively 2,073,600 pixels, and take 294 PPI at 5" - effectively 921,600 pixels or less than half the number of pixels (44.5%), and the resulting significantly lower need for computing power to perform equally, in order to get twice the battery life.