Paramount

Fan preservation is likely better quality.

The 2011 Lionsgate Blu-ray is incredibly poor for every Original Trilogy film; older processed older DVD-era masters with heavy use of DNR, sharpening and edge enhancement with a really dull color grade. The 4K Blu-ray is miles better. The DTS-HD 5.1 across all three films appears to be the same on both the Blu-ray and 4K Blu-ray, and they appear to be the untouched theatrical 5.1 mixes. 

The Uncut version has more violence: https://www.movie-censorship.com/report.php?ID=256325

Paramount 4K Blu-ray. See caps
HDR/grading: nice, but some blown out
Encoding: inconsistent, smeared motion
DNR: inconsistent, frozen
Old Paramount Blu-ray is arguably a solid alternative choice

Paramount 4K Blu-ray mono is different version of the Blu-ray mono from the same old 2000 DVD transfer.

The 5.1 remix on the 4K Blu-ray is an appalling remix done by going wild with artificially generated stems from Park Road Post who were given the surviving mono to separate. The experience is jarring and fidelity to original mix in terms of level balance, directionality and impact is nonexistent. Not only does this sound painfully weird, but the Paramount mixers then did whatever they wanted in terms of LFE, sound pans and effect changes.
The original mono mix was not restored and still needs it badly. The 4K master is filled with frozen grain examples coming and going plus some HDR issues in addition to the usual Paramount problems. It is simultaneously better and worse than the Blu-ray master.

> Paramount US. Overall good, superior compression to the US disc

Paramount/Universal 4K Blu-ray but: it has a few shots that are blurrier than the older Blu-ray, for unknown reasons see BR post.

Director's: US Paramount Blu-ray > WB Blu-ray

Paramount/Plaion Spain/Italy 4K Blu-ray has better encoding than the US 4K Blu-ray.

The EUR 4K has missing dialog.

Paramount US vs Entertainment in Video UK - comparison. From nicolas

I think this film is strikingly ugly and it ultimately doesn't matter much which one to take. Paramount's looks low-pass filtered (as usual) which Entertainment in Video doesn't have but it looks like they did some filtering of the chroma but compression-wise, both could be better.