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The two most popular display technologies used on modern smartphones are currently LCD (most often IPS based), and AMOLED. Both technologies have their pros and cons, though much of the market is starting to shift towards AMOLED due to its numerous benefits in the areas of color reproduction.
With AMOLED displays, each pixel is able to produce its own light, using red. green, and blue subpixels. This carries a major benefit that was often reserved for the highest end IPS displays targeted at graphic designers, which is effectively the benefits of RGB backlighting, but in the case of AMOLED, each pixel has this benefit. This all means that you can calibrate the color, as well as more freely change the color temperature of the display while keeping any loss in brightness to the absolute minimum.
Another benefit of AMOLED, is that you can push the display driver to the limit, within the working current range of the subpixels, the more accurately you can control them, the wider more color standards you can conform to.
In the case of the Axon 7, this means coverage of the majority of the human vision range, and sometimes more.
In the graph below, the solid gray line represents the possible surface colors as detailed by the International Commission on Illumination, and the colored line represents the range of colors that the display was able to produce based on the tested color patches (around 1500 measurements). The dotted lines represent colors within the tested color standards.
The ultimate benefit of having such a wide color range, is that if you are able to load custom ICC profiles, you can have the display conform to nearly all of the popular color standards
Beyond the color benefits, you also have space savings as you no longer need a backlight (this also means no more backlight bleed), as well as any polarizing filters. Furthermore, since every single pixel produces its own light, you save power when when ever you are displaying black, or simply displaying barker shades, as anything that does not require the full brightness of a pixel, will translate to lower power consumption for that pixel.
Overall, the benefits are numerous for AMOLED, but there are a few cons. AMOLED displays will get burn in faster than an LCD panel, thus they are less desirable for displaying lots of static content, though this trade-off is often accepted since people who will do something like have a news station logo get burned into the display, will likely watch that station enough to do the same to an IPS LCD panel.
LCD panels are another highly popular display technology, and are cheaper to produce than AMOLED panels. It is harder to get them to cover a wide color gamut, thus you will often see most low to mid priced panels approach or slightly exceed just the sRGB range but not quite cover wider gamuts such as what is found in the AdobeRGB standard. With LCD panels, another common behavior you will notice, is the lack of being able to do true black. Since the backlight has to cover the entire display, the panel is always trying to hold back the light when doing black.
Gamut of the Axon pro: (did well with sRGB, but cannot really be made to properly cover a standard such as Adobe RGB)
Even on some higher end TVs which may use full array LED backlighting where local dimming can take place, that function will not work down to the pixel level, thus in some cases, you may notice a halo around objects when it is used on such a display.
While the IPS LCD panels used in many smartphones may have a harder time reproducing a wide color gamut, they have a few benefits over AMOLED. The first and probably biggest, is that it is harder to get burn in on an IPS LCD panel. It is still possible (even though some people may say it is not, they likely have not seen an IPS display that was effectively used to watch the news for 90% of its active time for 2 years gifv clip showing just that for a TV that was left on CNN for too long IPS panel burn-in GIF | Create, Discover and Share on Gfycat
Overall, in terms of static content, an IPS panel can take much more abuse before takes permanent damage.
Another benefit with LCD is that if your goal is purely max brightness, using highly efficient white LEDs, you can achieve a higher max brightness, though this will often come at the cost of having less control over your color temperature, as well as being harder to get the exact calibration you want because you will be fighting the native output of the backlight.