As someone with a lowly 1080p projector and a 4k TV, I much prefer the 1080.
Viewsonic PX701HDH. I blow it up to 185" and I cannot see the pixels until I am uncomfortably close to the image.
The quality of the display/projector itself makes a huge difference. With a projector specifically - the bulb itself (and how much life left) is going to make a huge difference in picture quality.