There's a lot of variables not shared in your post. Did you rent the HD version of the movie or the SD version? Is your
TV connected directly to your TV or going through something else that might be using SD settings? Is the connections via HDMI cables or something else?
I just visited some relatives who had several 1080p HD sets in their home. Picture looks poor. I took a look at the connections and the cable company had connected the box with RG6 cable instead of HDMI. Thus, they were watching analog SD video on an HD set. Swap the cable to HDMI and the picture became HD.
It's also possible that that particular movie was just shot in such a way that higher resolution doesn't make it look very good. Your experiments with Netflix & Prime should give you enough of a content multi-sampling to find some well-shot video. You might also try movie trailers which generally look great in HD. If you have an iPhone, shoot some video yourself at 1080p or 4K, drop it into iTunes and then stream it to your TV via your
TV- that should also look really good.
If you happen to have a blu ray player and at least one movie disc, hook it up and look at some of that movie. Then hop into the iTunes rental store, locate the same movie and watch the (free) trailer to see if the picture looks comparable.