Thanks all.
Not sure what happened, maybe after a reboot, but contrast is almost the same now in windowed and full screen mode. 
Thanks for the link to the ICC profile, @FreeBirdJosh.
I also changed resolution to 4k and I set the resolution to 4k, which gave me more options for refresh rate, though maximum is 59Hz now. I can’t set it to 30Hz as suggested because in MSFS the FPS halves to 15FPS (no idea why). I use vsynch at 30FPS to smooth out my frame rate.
Setting the colour depth to 8bpc makes the MSFS window way to dark, so I’ll leave it at 10.
The problem I get with screenshots being overblown is still present though:
I can live with that though.