DVD

It has DCP showings but no Blu-ray releases.

Included in the Complete Kubrick box set with FiM encode of the same master from the WB release without the filtering, 1.85 ratio restored for US Cut; both US and International Cuts are 4K.

No Blu-ray or DVD release until the Criterion 4K Blu-ray has presented the US in its original theatrical aspect ratio of 1.85:1. The International Cut has never been presented in it's OAR of 1.66:1 in any home video releases.

The packaging on the back of the WB 4K Blu-ray incorrectly states it as 1.85:1 when the movie is actually 1.78:1 as is the original Blu-ray. 

Clarity Films DVD remastered by the Academy of Motion Picture Arts and Sciences in 2013

The DV/HDR grade is tasteful and not overdone. SC has better compression, though not flawless; encoded by FiM, but Criterion also holds up quite well. Both releases claim to be approved by Lynch.

SC has a missing fade that Criterion reinstated.

The film was originally mixed in Dolby Stereo (matrixed LCRS). For the 4K restoration, this mix has been transferred from the original magnetic elements and remastered with Lynch's supervision. Unfortunately, the fidelity suffered in the process, with many sections ending up significantly less detailed due to a noise reduction pass. This track has been altered compared to the original, with reverb added to some dialogue, different ambient sound effects, changed panning, and extended bass.

For the unrestored mix, there are two major options, each with its own merits and flaws. The 2001 Paramount DVD, which I would say is the best well-rounded mastering, and the 1999 Japanese LaserDisc, which has noticeably better clarity and high-end detail, as well as better dynamics, but suffers from occasional distortion and has less bass than the DVD.

The LD also has some ambiance buried too low in the mix, and some dialogue panned more to the centre than the DVD. There are no content changes I was able to find. Unfortunately, I don't know what accounts for those differences.

The other available tracks all have more significant flaws. The Italian and Japanese BDs use the same base mastering as the DVD, but with some patching in a few shots. HD-DVD is sourced from an inferior transfer, the same as the Momentum DVD.

The 5.1 remix, originally introduced on the 2002 DVD, and carried over without changes to the 2009 BD is a light and mostly faithful remix, with fairly minimal LFE and surround use, but still potentially worthwhile as the only discrete track.

Imprint Australia 4K Blu-ray has slightly better compression than Criterion 4K Blu-ray.

The master in DV looks all but identical to the Criterion’s HDR grade. Detail-wise, FiM’s encode looks like it uncovered a tiny bit of extra high-frequency information that got filtered on the Criterion. See nicolas review

1990 Criterion LaserDisc/1993 MGM LaserDisc/2002 R2 MGM DVD are the best. See blah-ray https://blah-ray.blogspot.com/2018/01/raging-bull-1980.html

Imprint Australia 4K Blu-ray has better audio than Criterion 4K Blu-ray, from nicolas:

I believe that what’s on Imprint’s 4K is one of the good mixes MGM and Criterion released during the LaserDisc days. Music is powerful and detailed, dialogues have excellent fidelity and ambient sounds have perceptible depth. I compared the "new" 2.0 with the anemic 5.1 as well as the Criterion 4K mix and could clearly hear the improvements.

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 color timing and Atmos remix are thankfully taming the excessively overdone terrible Blu-ray in those areas but neither is fully accurate. The Atmos remix sounds lifeless and essentially tames the crazy LFE of the Blu-ray remix that never stopped while also spreading the sound around overhead. The music is absolutely lifeless here. If it weren't for the visual changes it might be possible to regrade the picture master and just live with the encoding noise. As it is, purists will want the LaserDisc, DVD or Japan WOWOW broadcast of the Laser Pacific master which is the same master used for the awful Blu-ray just without the hideous color grading applied.
The DVD was handled by Lowry Digital and is overscrubbed like crazy plus had all sorts of DVD era edge enhancement and other issues. It instigated the digital changes of the boulder rod and snake reflection removals. The ONLY widescreen versions of the film without ANY changes are the 1992 LaserDisc and the 1999 final release VHS.

Audio wise, Raiders is EXTREMELY complex. Like the Star Wars trilogy it had three specific release mixes with variations and differences plus a fourth mix that was not used. The mono mix had unique bits and has never been officially released though you can hear bits of it on the 2003 bonus DVD and in the Raiders in Concert live symphony performances. The Dolby Stereo is roughly what was used on all pre-widescreen editions on VHS, Beta and LaserDisc in the 80's. The best iteration of that is the 1991 Japan LaserDisc reissue with PCM digital sound. This iteration is more of a home version as it doesn't really have much surround. Yet it retains dynamic range unlike the 1985 home video remix of Star Wars' Dolby Stereo track. The 70mm Dolby six track magnetic audio was supposedly used in making the excellent sounding 5.1 made for the DVD release. Before the release the film was mixed in the very short lived VistaSonic process which was Paramount backed. This was dropped very last minute as the system had tons of playback issues and the film was apparently hastily remixed in Dolby formats. When the first letterboxed transfer showed up on the 1992 Paramount LaserDisc release all of a sudden the Dolby Surround encoded matrix track it contained is without question the best sounding mix of Raiders you can find anywhere. It is more aggressive than the Dolby Stereo, more punchy than the DVD 5.1 and even contains a unique different sound effect which indicates it is clearly a different mix. It is unknown if this is the abandoned VistaSonic mix or a new quiet Dolby Surround home mix akin to the 1993 Star Wars Definitive Collection remix. To this day, the LaserDisc Dolby surround is the best sounding version of Raiders you are likely ever to hear. Even though it isn't discrete.
The Blu-ray remix though supervised by Ben Burtt went overboard on making everything aggressive and modernized. The LFE is virtually nonstop even in dialogue scenes. It is a textbook case of revisionist audio desecration. The 4K Blu-ray Atmos merely tames the LFE and reduces impact even more by moving around more elements and adding more processing. Both of these remixes are a crime.

DFIC extensive review: https://youtu.be/evsrJOTIjdA

R1 DVD has the original Dolby Stereo 2.0 mix and a more faithful 5.1 presentation (possibly from 6-track)