TSPDT

MoC slightly better than Criterion http://www.dvdbeaver.com/film5/blu-ray_reviews_69/kwaidan_blu-ray.htm

StudioCanal and Universal Blu-ray have DNR. 4K master also exists, unreleased

Carlito’s Way was released theatrically in both Dolby Stereo and DTS. The 2.0 on the Arrow UHD is the original stereo mix, unknown if the 5.1 mix on the  Arrow disc is the original DTS mix.

Italy Plaion 4K Blu-ray > Paramount 4K Blu-ray (marginally)

BFI Chantal Akerman: Volume 2 Blu-ray or US Icarus Blu-ray but no comparisons

Germany Blu-ray and Criterion Paramount no difference, just get Criterion https://caps-a-holic.com/c.php?d1=11014&d2=10022&c=4022

Germany Blu-ray has English audio 

Germany Blu-ray is part of a 3-film box set like the Criterion but by StudioCanal 

4K restoration has no home media release yet

Arrow has a different grade and a better encode than the Shout! Factory, though the difference in either is not major. Imprint release, which leaves Shout! Factory's master and subtitles as is, is encoded by FiM. https://forum.blu-ray.com/showpost.php?p=24473097&postcount=56

Original mix: Shout! Factory 4K Blu-ray (similar to Criterion LaserDisc, but less distorted)

Alternate mix: Scanbox Nordic PAL DVD

Surround remix: HK Video France 4K Blu-ray (5.0)

Arrow used the alternate mix, but with extra filtering and lowered dynamic range. The alternate mix has much better fidelity.

Imprint presumably used the Shout! Factory original mix and left it as is, though no official confirmation.

Arrow has a much better translation.

Arrow LE has the Taiwan Extended Cut which will not be present on the standard edition. However, Imprint is FiM and has its own archival extras not present on the Arrow.

The Paramount 4K "restoration" is a desecration. It has completely revisionist color timing, harsh HDR, treatment of stock footage, bad encoding, selective DNR and grain management so bad that the entire screen frequently freezes up with only characters moving around in grain soup. It is so bad that the film's restorer Robert Harris publicly washed his hands of it saying essentially the 2007 restoration (with Willis and Coppola supervising) is how the film was intended and made. This is Paramount's modern version done their way. The new 1080p SDR Blu-rays in print are the crap 4K desecration master with the same problems still there just harder to spot and with crap encodes. Part III fares best of the three and these issues are at their most minimal-but they're still there. The new Coda version is given prominence with lesser encodes for the other two versions. The original mix was remixed into 5.1 decades ago and we have yet another version of this instead of the original Dolby Stereo SR as heard on the LaserDisc release.
The 2008 Blu-ray of the 2007 restoration, while an imperfect outdated disc, is LIGHT YEARS better than this 4K desecration. The only truly major issue is that it is very slightly redder than the 2007 finished master as seen on DCPs.
DFIC review of the hideous crap 4K Blu-rays: https://youtu.be/0uw6-Kcy_UA?si=ob1nDg0wTCvemjH0

Despite being restored alongside the Coppola Restorations of The Godfather: Parts I and II, the Part III restoration is not officially labelled a Coppola Restoration.

France ARTE has Costa-Gavras Coffret boxset Germany/Spain also have releases

4K Blu-ray caveat: mostly great video but the 4K Blu-rays have had additional DNR applied in some scenes on top of the DNR that had been applied in post-production and was already present on the DVDs & Blu-rays

The 2020 Blu-ray may be better than the 4K Blu-ray?

New Line Blu-ray have the original 6.1 mixes

4K Blu-ray set is missing extras from the old Blu-ray/DVD releases