Worse picture quality but much better immersion. I am also using a video projector and the fact the picture is taking one entire wall makes a difference regardless of the actual resolution.
Picture quality doesn't matter a lot when you are watching a movie from the preHD/4K era anyway. It is even better as you are less subject to aliasing.
I wouldn't trade immersion for resolution. Also one doesn't feel a lack of picture quality when not used to it. I don't own a 4K screen. So I don't miss 4K quality and watch movies with the utmost quality I know. Ignorance can be bliss.
Added bonus is you don't have a huge black rectangle in your living room when it is turned off, only a tiny device (that can easily be hidden).
Having said that I heard there are pretty decent laser 4K video projector these days with HDR support.