Effect of screen shape on video quality
I do not understand your question. As it is I would say nothing.

Get a 16x9 inches monitor. It measures 16 x 9 inches. Now rotate it 90°. It has the exact same total displaying area but now measures 9 x 16 inches. The "optimal" viewing distance is the same.



If you are referring to different aspect ratios, the unit that is important and easier to get is the native linear PPI.

Find out the horizontal resolution used and divide it by the horizontal physical measure of the display area.

If your monitor has 1920 x 1080 px, use 1920.
If the monitor measures 21 inches on the horizontal size:
1920/21 = 91.4 PPI. Use that value to compare other monitors.