A large portion of the U.S. projector base is still 2K digital, about 60% I think is 4K. There are some really awful early Barco projectors out there still with horrible contrast ratio. They would all be 16:9, but the cheap theatres will not have the necessary setup to do ~2.35:1 anamorphic properly. It is probably not the resolution though that is bad, the brightness/contrast of early or cheaper digital projectors was poor and cheap movie houses will not replace their bulbs often enough ... which fortunately newer projectors are moving away from.
The newer theater 4K HDR projectors are quite good, every bit as good as 35mm film. 8K projectors are on the horizon and will have effective image quality on par with 70mm. 8K digital cameras are already in production. 70mm has lots of raw resolution, but shake/shudder from the mechanical movement means the real useful resolution is degraded a fair amount from the single image resolution. That lack of shake/shudder is also makes 3D work better.
Having seen the best of digital cinema projectors and what are likely some of the best home projectors, I won’t say home theater is better and certainly not way better. Modern 4K cinema projectors with "laser" light sources are exceptionally good. Then again, so are the latest JVC home ones. Both need good screens, and that is one area home setups are often lacking. All black environments to minimize reflections and maximize contrast don’t have high spouse factors :-) I do believe that popping my corn in ghee may taste even better than whatever they use at movie theaters though :-)
Jordan B Peterson? ... just don’t get him started on religion, then he sounds like an uneducated zealot :-)