I fell down the LOTR home release color grade rabbit hole yesterday.

tl;dr there is and will never be a good HD version of these movies.

The theatrical blu-ray looks fine, but it doesn't have the extended scenes. They did add noise reduction to remove film grain, but it doesn't impact it too much.

When the extended cut was released on blu-ray (2012), they fucked with the color grading. 1 is green'd while 2+3 are sepia'd. Best case scenario is 2nd pic, where it brings out detail in skin and hair. I would argue it still looks like shit, because the rest of the scene is blue and there shouldn't be that much red visible in the dramatic moonlit shot.

The 4k HDR version readjusted the colors back to what they should be (looks dull in 1st pic bc HDR->SDR, but you can tell the sky is blue and not green), but added loads of noise reduction and aggressive digital sharpening (pic 3, zoomed in).
When the original movies were shot on 35mm film, they added fake grain to the CGI to make everything look fucking sweet. This has contributed BIGLY to 2001 renders holding up 20 years later.
So for the 4k release, they naturally applied the most aggressive digital noise reduction to sandblast all film grain and taking the detail away with it. Pic 4 is all CGI and looks like terrible CG from 2001 in the 4k version. This """"remaster"""" was also released in 1080p so everyone can have the displeasure of seeing this version.

Many attempts were made to make the latest release look like it was NOT shot on film. Peter Jackson and the original cinematographer signed off on this specifically to make it look like the Hobbit movies (which were digital (and sucked lmao)). As long as they're still alive every release is going to fuck with the films more and more. There are other scenes adjusted to be consistent with the prequel trilogy as well. Wait, why did that last sentence sound familiar? Why is Peter Jackson's beard looking a lot whiter? Oh no, oh god, oh no