The important thing with video levels is that the output and display levels match.
- Full range is 0-255
- Limited range is 16-235
Full out/limited display = clipped shadows and highlights, overly dark/contrasted image:
Limited out/full display = washed-out image:
Limited out/display limited = perfect image.
Full out/display full = perfect image.
The main reason the different ranges exist is that PC has always used the full 0-255 8-bit signal for video output, while video intentionally used a limited 16-235 range because it allows for "below-black" and "above white" information to be present in the signal.
Technically you have the potential for smoother gradation with full out/display full, because you have 256 steps of gradation in use vs 220 and are avoiding a conversion step if using a PC/Console (internally rendering full-range) but it's probably not going to even be visible on most displays.
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Many video devices have problems passing through full range signals and will automatically clip/convert the signal as it passes through. This can result in an image with crushed shadow/highlight detail, but one which does not have the typical overly-contrasted appearance you might expect:
It's generally a lot easier to stick with a limited output on every device where possible - especially when you now have devices doing things like switching between SDR and HDR outputs on the same display input.