Paramount

Gaumont Blu-ray is better encoded than Paramount but graded very teal see caps

France StudioCanal Blu-ray has worse encoding and is more cropped at top and bottom see caps

US Paramount > International Warner Bros Blu-ray

International Warner Bros Blu-ray has a lossless PCM 5.1 track

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 II overall fares better than the first film but it has all the same problems. Randomly some shots are the worst in the trilogy looks mushy and manipulated to death.
The mono option is an unnecessarily processed version of the lossy mono from the 2008 Blu-ray. The 2008 Blu-ray of the 2007 Coppola Restoration while an imperfect outdated disc is LIGHT YEARS better than this 4K desecration.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. The lossy mono on the 2008 Blu-ray is the best version of the original mix known to exist as it is better than the late 80's mastering for VHS and LaserDisc.
DFIC review of the hideous crap 4K Blu-rays: https://youtu.be/0uw6-Kcy_UA?si=ob1nDg0wTCvemjH0

Old Paramount Blu-ray better than new 4K Blu-ray: smeary grain/detail, poor contrast

4K Blu-ray and New Blu-ray has lossless TrueHD, Old Blu-ray just has lossy Dolby Digital

(Britain release only has 5.1)

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.
The mono option is an unnecessarily processed version of the lossy mono from the 2008 Blu-ray. The 2008 Blu-ray of the 2007 Coppola 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. The lossy mono on the 2008 Blu-ray is the best version of the original mix known to exist as it is better than the late 80's mastering for VHS and LaserDisc.
DFIC review of the hideous crap 4K Blu-rays: https://youtu.be/0uw6-Kcy_UA?si=ob1nDg0wTCvemjH0

Same master, but less bitrate starved.

The encode on the BD is preferable to the UHD. Same master, but less bitrate starved: https://x.com/SadHillDevan/status/1530057783885721607?s=20 and see caps

4K Blu-ray is AI upscaled

The 4K Blu-ray bonus disc, the 2012 Blu-ray bonus disc, and the 2005 3 disc DVD have exclusive extras.