2010 US Kino Lorber or 2012 UK Artificial Eye

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.

Criterion US Blu-ray

4K restoration: Koch Media DE 4K Blu-ray
Original digital master: Cannes 2006 Promo HD-DVD

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

Remixed 5.1: The Jokers FR 4K Blu-ray
Original 5.1: Cannes 2006 Promo HD-DVD

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.

Criterion 4K Blu-ray

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

Original mono is on the 1996 Japan DVD and 2005 Spain Boxset DVD. But 2008 Criterion Blu-ray’s 5.1 remix at least is in the correct pitch. All 5.1 tracks on later 4K-resto BDs have a raised pitch. Furthermore, the 2008 5.1 and 4K-resto 5.1 differ in content in the scene where Tony Leung drinks coffee in slow-mo, with the 2008 version having only background / ambient sound, while the 4K-resto version plays Faye Wong’s song. Note that it's quite easy to pitch correct the 4K-resto 5.1 to match the original pitch and only a delay adjustment is needed to sync.

2012 Criterion Blu-ray, 4K Blu-ray unrecommended because of controversial colours, no HDR, minimal resolution uptick, and DNR master

2012 Criterion Blu-ray is the most accurate, but some may prefer the Criterion 4K Blu-ray

2002 Criterion DVD for original Dolby Digital 5.0 theatrical. The 4K Blu-ray 5.1 adds additional foley and effects.