You're shining a bright light on a wall, which you are looking at.
With a monitor you are shining a bright light at your face, while staring directly at the lightbulb!
If you're using a monitor in the dark the way you use a projector, you should turn the backlight down. If you're using it in a well lit room, the brighter backlight should have less of an effect.
It sounds to me you've never actually looked at a monitor display large swaths of white before, it's brighter than light hitting a wall for sure, even with the brightness down, extra so when the ambient lightning is dark too.
The fact that it's bright outside when the sun is up might help, but it's nowhere near enough to compensate!