Wong Kar-Wai

Criterion 4K Blu-ray has original SDR master while Plaion Germany and France has a subtle additional HDR-regrade. Either one is good depending on user preference.
Important to note, Criterion 4K Blu-ray still has different color timing from 2008 Criterion Blu-ray see https://caps-a-holic.com/c.php?go=1&a=0&d1=15680&d2=15679&s1=165346&s2=165329&i=10&l=0

2017 JP Kadokawa Blu-ray has the best encoding out of all the older discs.

Kino Lorber and Artificial Eye Blu-ray use the same master, between the two the PQ on Kino's release is slightly better, but the difference is negligible.

The 4K restoration (Criterion, 4K etc) are cropped to 2.35:1, have revisionistic colour grading and other changes.

Caps: old master, old master vs 4K restoration

Wong Kar-Wai on the framing:

With Fallen Angels, I have changed the format to cinemascope, because it was originally what I had intended to release the film in. When we were cutting the film, we accidentally turned the Steenbeck on anamorphic instead of standard. I felt that the film looked much more interesting because it enhanced the distance of the characters on top of the extreme wide angle that we shot on. Back then, it was impossible to shoot a film in standard and release it in anamorphic. With this restoration, we have successfully fulfilled this wish.

2012 Criterion Blu-ray is the most accurate

4K Blu-ray unrecommended because of controversial colours, no HDR, minimal resolution uptick, and DNR master

The 4K Blu-ray 5.1 adds additional foley and effects.

4K remaster is cropped 2.35:1 from the original 2.55:1 presentation, and has significantly different color grading, as is the case with most WKW supervised restorations. Due to DNR the detail is sometimes lacklustre compared to the old master. CGI scenes appear to be rerendered. A sepia tinted scene was altered to be fully black and white.

Caps: Criterion US BD vs Cannes HD-DVD, HD-DVD vs KR BD vs DVDs vs US BD

The remixed track has different front panning and little LFE use compared to the original.

HD-DVD is by far the best option for the original track, as DVDs and Korean BD suffer from noise gating, limiting and duplicated surrounds. Remixed tracks are all similar, but French disc has slightly better dynamics, particularly on the LFE channel.

The 2006 HD-DVD is a promotional release made in only 100 copies, handed out to VIPs at Cannes Film Festival. See this blog post for details. The same master can be found on KR BD, though it suffers from interlacing, blended frames and a gamma bug, as well as older DVD releases.