LaserDisc

Paramount US 4K Blu-ray > Capelight DE 4K Blu-ray (caps)

Although the provenance of Paramount's 5.1 track is not confirmed, the fidelity is outstanding and speaks for itself.
The 7.1 track on the Capelight/old Lionsgate release is just an upmix with nothing gained over the 5.1.
The original stereo mix is only present on older DVDs and LaserDiscs; all Blu-ray 2.0 tracks are downmixes.

Paramount 4K Blu-ray has no extras, Capelight 4K Blu-ray has most of the extras, Olive Films Blu-ray has a exclusive commentary

5.1 is the same on all Blu-rays

Touchstone Home Video US LaserDisc [940 CS] has the original stereo

Japan 4K Blu-ray beats the other 4Ks and includes English subtitles

All 4K releases are upscales of the same master with a substantial amount of DNR.

Due to budgetary constraints, the original theatrical mix was mono. It was replaced with Dolby Surround for all subsequent releases and was never re-released.

LaserDisc is the best souning version of the original home video mix, as all later releases attentuate bass significantly and lower dynamic range. Comparison

The Japanese audio was remixed in 5.1 twice, first time in 2001 for the DVD release, and second time in 2009 for the BD release ("Hypersonic" remix). While the 2001 remix remains mostly faithful to the 1988 mix, the 2009 Hypersonic remix is highly revisionistic. However, its fidelity is outstanding, and despite many changes made, it's a worthwhile alternative experience for fans of the film. The 4K release includes the Hypersonic mix, but with a tonne of unnecessary noise reduction and unbalanced levels.

Comparison between mixes, list of changes between mixes

Film Whisperer's restoration is better

Censorship changes for Blu-ray: https://www.movie-censorship.com/report.php?ID=224122

Germany Capelight 4K Blu-ray or Australia Via Vision? > US MVD

The original Kiyoshi Kurosawa cut, which was the version given a theatrical release, has not seen a home release in any form, as the film was later recut for the home video and TV releases by the film's producer, Juzo Itami.

Shout! Factory 4K Blu-ray (caps)

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. There was also a rare SVHS release using the letterbox LaserDisc master.
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, Last Crusade had Dolby 70mm with stereo surrounds, Dolby Stereo SR for 35mm and was mixed in a THX sound theater to ensure the ultimate in technical quality in 1989. The DVD was supposedly made from the 70mm mix and the Blu-ray 5.1 seems to bring that into lossless. This is unconfirmed but each seems to be a healthy and accurate version of the original audio. However, the LaserDisc despite only having matrix PCM stereo is punchier and livelier as a listening experience. Despite not being discrete it arguably sounds better than the 5.1 versions. Some who remember seeing each of the original release versions claim to remember the 35mm Dolby DR as sounding better than the 70mm Dolby.  This is a case where both sound great and it's up to fans to decide which they prefer. Both are essential for any Indy collection and the LaserDisc is very cheap. The VHS hifi seems to be the same 2.0 matrix with format differences so it can also be compared against the DVD and Blu-ray 5.1 versions.

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

MGM 5.1 remix noticeably reduces elements of original mix

WB 4K Blu-ray but with notable color timing issues

Original mix on VHS, LaserDisc and DVD is significantly warmer and more impactful sounding. These nuances are lost on the 2005 remaster audio found on DVD and Blu-ray which due have a tinge of extra clarity in contrast.

The Atmos mix is excruciatingly bad as it removes original sound effects and wrecks the original sound design. Music is prioritized and dominates in a bad way. The sound library effects used to create a specific sound signature as part of the mix of time period production design is completely lost. Fidelity is also lowered due to noise reduction and processing.

2012 US Disney Blu-ray has dubtitles. US GKIDS Blu-ray has bonuses that are absent on the US Disney Blu-ray

Eagle Pictures Italy 4K Blu-ray > StudioCanal 4K Blu-ray: better compression than StudioCanal

Disney 4K Blu-ray's artificial smoothening of facial textures making actors look unnatural, grain reduction and other changes to make the film look less like a product of its time

Old WEB-DL or HDTV rip for non AI version

Japan LaserDisc is in Dolby Stereo

Japan LaserDisc is an extended cut approximately 7 minutes longer than the theatrical cut on the US LaserDisc