I've always thought that arcdegrees should be what we measure UI's in: how much of a user's field of view does this thing consume? After all, what makes text "small" is that how much of my FoV it consumes (or doesn't). Not inches, or points, or pixels.

(Admittedly, "points" are still likely a good measurement for print. Perhaps one can work backwards and fudge point as a measure of angle if you consider 12 point font at a typical viewing distance.)

I assume the real hard piece is figuring out the distance the display is going to be viewed at. Some definite defaults exist (phones are typically about the same distance away, same with desktop monitors) but unique situations certainly can exist. (I'm also assuming that the monitor can report it's physical size and resolution; combined w/ viewing distance, it should be possible to calculate FoV.) If you did this, you should be able to mostly seemlessly split a window between two displays, and have it be equal "size" in the FoV. (of course, some displays have borders, so that fudges it a bit.)