I've been running some tests lately (2H2020) concerning reducing the size of some high quality movies of my collection, just for PC to TV 1080p viewing, from 20-30mbps videos to 2-3mbps ones. To that end, I run some ffmpeg (latest gyan.dev version at the time) tests comparing same-bitrate encodes between: codecs (x264,x265,VP9,AV1), presets (slow, slower etc), CRF's (21,22,23,24 etc) and encoding colorspace (8bit, 10bit, 12bit), where applicable. I have arrived at the following combination as my personal preference:
• x265. This is always better than x264 bitwise. It's also worse than aom-av1, but aom-av1 is not optimized to work on all CPU cores, therefore aom-av1 is time-expensive in the end. Unless you run multiple encodes at the same time, which in this case I can also recommend AV1.
• Preset slow (on x265). If you have a fast machine (I don't), you can go to slower. But from then on, it's not worth the CPU-time (as I found in my tests).
• CRF 24. That's my sweet spot for final movie size. Higher CRF's create smaller files (and I found they encoded faster), and lower CRF's create bigger files (and slower encodes). No big deal here, this was expected.
• 12bit colorspace. Here's the good part. In some of my test encodes (for example in Bosphorus_1920x1080_120fps_420_8bit_YUV.y4m), 10bit encode provided 2% smaller and VMAF better results. But, in most other commercial clips I did some testing, I found that 12bit encoding gives better results (smaller size AND better VMAF). It goes without talking that they both are better than 8bit encoding of those 8bit source videos. If you go to 10bit source videos, 12bit encoding also gives better results than 10bit encoding. I'm no master at why this happens, the other answers provide some insight to that, but I also did some screenshots comparison of comparable size 8bit/10bit/12bit encodes of 8bit/10bit content, and I consistently liked the 12bit encodes more. They provided smoother gradients where 8bit encoding showed banding. Now the drawback is that going for 10bit/12bit encodes, you may lose hardware-decoding capabilities for the device used for playback (my PC loses hardware playback capability at 12bit), but for my target usage (lowest acceptable quality for small size), the above combination (x265,12bit,slow preset,CRF24) is my sweet spot.
That was my experience, backed by extensive testing, feel free to run some tests yourself.