It looks like you are encountering this bug after all, where text is scaled using the Windows DPI settings, but the rest of the UI is not, as it causes the text to be much larger than the rest of the UI.
What happens is that if Windows was set to 200% size, selecting 150% size in Media Center displays the UI elements at 150%, but the text is now scaled to 300% size, as it is being scaled up twice.
As a temporary fix, go to Tools → Options → Tree & View → Select font… (last item on the list)
The standard font is 9pt SegoeUI.
Since you are saying that the UI elements are too small at 150% size, I am guessing that Windows is set to 200% size.
Since Windows is at 200% size, we need to halve the font setting in Media Center. (if it was at 150% size, it would be 9 ÷ 1.5 = 6pt)
Ideally it would be 4.5 but only integer values are supported. Enter either 4 or 5 for the text size.
Text will not display correctly until you restart Media Center - this DPI scaling bug only seems to apply when you launch the program, not when you make font changes.
Since you will be setting Media Center to 200% size, this results in:
4pt: 4x2 (DPI settings) x2 (Media Center size) = 16pt text
5pt: 5x2 (DPI settings) x2 (Media Center size) = 20pt text
So text will be scaled to being either slightly larger, or slightly smaller than the ideal size for 200%. (which would be 18pt, since the standard size at 100% is 9pt)
This really needs to be fixed.
Media Center should not be changing the font size based on Windows' DPI settings.
It should be changing the entire UI size, so that the "100%" setting in Media Center is equal to your DPI scale. (e.g. 150% or 200%)
Either that, or the size options need to be expanded to allow for the selection of up to 400% scale, and the size setting in Media Center would match the DPI scale.