Blu-ray

4K restoration

There's also 4K Streaming but no comparison is available

Eureka release has a better encode, but is taken from an older master. The Criterion Blu-ray was a new restoration from the ground up, and is substantially improved despite not being as well encoded.

2K transfer, not sure about France

caps; UK and US Blu-rays share the encode

251 min cut (Extended): Fox Blu-ray. Eagle Pictures has forced Italian subs in some parts

229 min cut (Theatrical): WB Blu-ray

139 min cut (US theatrical): VHS

Eagle Pictures 4K Blu-ray, caps

The 4K includes both theatrical and extended cuts. It's overall a solid upgrade over previous discs, but some will strongly dislike the color grading.
There are some issues with encoding and grain management.

Nic's review:

Some definitely messed with it as there’s grain management going on that resulted in magnetic, squishy grain movement. Both cuts (4K discs) are affected and it doesn’t look like an encoding issue to me as the bitrates don’t drop down to single digits á la Paramount or StudioCanal. During opticals, the lowest I’ve noted on the Extended 4K was around 30 MB/s vs. ~5 MB/s more for the theatrical cut.

Darker scenes are mostly (but not always) better but when it gets brighter, particularly in exteriors or scenes like the Jennifer Connelly dance scene at minute 38, I can’t unsee the digital tinkering as it does some damage texturally.

I compared it with the Eagle Pictures and Warner Bros Fox Blu-ray of the extended cut and they all look fine without grain management like that. Eagle Pictures’s Blu-ray is an older one if anyone’s curious and credited to another authoring house than 64Biz, which did the 4K.

Other than that, except for some encoding-related chroma noise that peeks through in the DV layer, Eagle Pictures did everything right. They corrected the framing to 1.85, kept the original English titles, the English restoration note, subtitles, HDR/DV is gentle and respectful of the source black levels are better than on the Warner Bros/Fox Blu-ray. Without that grain management, this would’ve been the all-timer release we all longed for.

251 min cut: Fox Blu-ray (24-bit, Eagle Pictures is 16-bit, not audible)
229 min cut: Warner Bros LaserDisc (missing 2 minutes, but original mono mix was never released on DVD/Blu-ray)

Extended edition adds scenes cut from the theatrical, but from a much lower quality source. It's intended to approximate the original cut, but to what extent that is true is debatable.
US theatrical cut is infamously bad, was panned at release and never re-released on home video.

The Paramount 4K master is HEAVILY revisionist in that all of the effects and opticals were redone and tweaked with errors and issues. There has been grain management (moments of stagnating grain and haloing) and the encoding isn't great hence the typical Paramount noise in the image. (especially skies) The HDR is a bit bright in the highlights. The Blu-ray is showing its age but does not have any of these digital alterations. It is from the scan done by Laser Pacific and is the highest quality unaltered master we have. The DVD was done by Lowry Digital and had much scrubbing and processing of grain in addition to edge enhancement. The letterbox LaserDisc was the first widescreen release and is very good for its time.
The 4K Blu-ray audio is seemingly an Atmos remix of the 5.1 found on the Blu-ray which itself is very similar to the DVD 5.1. All are presumably based on the 70mm Dolby six track mix. The Atmos is more processed and moves the sound around more so it is inferior to the older 5.1 iterations. On release Temple of Doom had 70mm, 35mm Dolby Stereo and mono mixes. The mono was for 16mm and other outlets and is presumably close to if not a mixdown of the stereo. It is seemingly the last Lucasfilm title that had a mono mix made. The Dolby Stereo is one of the most aggressive matrix mixes ever made and is still a blast to this day on the letterbox LaserDisc release. It is more aggressive than any of the 5.1 discrete versions which is either due to studios taming the audio later or the 35mm mix being handled a bit differently to the 70mm mix. In terms of releases today, the LaserDisc still sounds better than DVD, Blu-ray or 4K Blu-ray because of this factor.

DFIC extensive review: https://youtu.be/evsrJOTIjdA?si=wtdWGxZBfhPYTIeW

Sony 2022 boxset or 2024 VHS packaging has Dolby Vision, 2019 Sony 4K Blu-ray is HDR10 only.