It is better. But the difference between full HD at 135 inches vs 4k at 65 is pretty significant in terms of the immersive effect even if you need to sacrifice on pure picture quality . Plus sometimes it is not the resolution that is making it look better, it is the overall processing. My old Kuro is not 4k but none of these $1500 4k sets can touch it for picture quality even if the signal is 4k. But in the end it depends on your taste and circumstances. There really is no one "best way to go".
To add to this the pixel shifting 4K projectors are generally excellent. It's probably nearly impossible to detect native 4K from pixel shifting 4K on most implementations. But the cost can be much lower. A projector like the Epson 4010 is a little over $2K with 2400 lumens. Its a 4k pixel shifting projector with 1080p native panels that is pretty much indistinguishable form more expensive native 4K panels as far as resolution is concerned. This unit can give you a huge picture.
Alright... since we are going there anyway. You seem to know your stuff on projectors. I'll bite.
This weekend I spent my whole Saturday wiring up my new Paradigm Prestige surround system with Anthem MRX 720 that has two 4K HDMI outs.
We are watching John Wick in a darkened 15 x 17(wide) room. And my beautiful 55" OLED is recessed mounted on a wall that must be at least 12 feet on the diagonal. Gosh if I didn't find myself staring at all of that white space.
If I'm going to be getting a guy to wire in my Atmos speakers into the ceiling, he could perhaps put a power & HDMI up there too. What would you consider if you were:
1) buying a projector now, and
2) maybe thinking this is a project to be fulfilled in ~2 years... worth waiting for 4K HDR projectors to drop in price?
Give me the "this is the sweet spot for price/performance" answer that only an enthusiast like you would know. I would need a retractable screen too (so that the TV can be behind the screen and available for "daily" use... kids use this room during the day).