As CB I was a Golden Harvest production, Fortune Star owns almost all distribution rights worldwide except for the US, where Fox handled US theatrical while HBO (later merged into Warner) handled video distribution. The European and Asian DVD releases use Golden Harvest's international print, and while most feature the English mono in addition to foreign language dubs, most of them ether have a vintage Golden Harvest logo or a Media Asia (who owned the GH catalog prior to Fortune Star) indent in leu of the 20th Century Fox logo variant that has the driving mayhem around the tower and Burt's laugh. Keep in mind that I've also heard some of the European DVDs have redone localized credits of the video generated kind, while one of the early non-anamorphic Megastar DVDs (reportedly being a PAL-NTSC standards conversion of a VCD master and only containing badly upmixed Cantonese and Mandarian 5.1 audio tracks) use a Golden Harvest Hong Kong release print with theatrical printed English+Cantonese subs.
The HBO VHS releases and their 2001 DVD are of the US version opening with the Fox logo variant. Their older video releases (including the HBO laserdiscs) should sport the original mono while starting with the DVD release (sporting a anamorphic widescreen transfer in 1.85), the mono got dropped for the 5.1 remix in addition to a 2.0 fold-down of the latter. The 2011 US BD (also from HBO/WHV) sports a 2k HD scan of an US IP in 1.78:1 and opening with the Fox vairant, but again only offers the 5.1 remix in lieu of the original mono. The UK Medium-Rare DVD & BD was released in 2013 under licence from Fortune Star, followed by BD releases from Tobis in Germany and Umbrella in Australia. These releases all use the same 1.78 master as the US BD and offer the English track in 5.1 in addition to foreign dubs (medium Rare also features a Eng PCM 2.0 downmix of the 5.1), but all trim off the Fox logo variant in lieu of a Fortune Star + vintage Golden Harvest combo (which in all, still manages to brings up the feature R/T another 20 secs or so).
The sequel was put out theatrically by Warner in the US, while GH through local distributors overseas. It seems all VHS and DVD releases worldwide sport the same transfer (opening logos aside) and feature the original English mono to a degree. The BD releases by Medium Rare and Umbrella in the UK and Australia respectively are licensed from Fortune Star, and in an odd twist from Fortune Star's usual upscaled specials, CB II uses a proper HD transfer of and IP and sports the original English mono. Only issues are it's mono track suffers "The Creepshow Effect" and the original Warner logos are missing.