They’re different mixes for the most part, the monos being the ones that were OK’d by the Fab Four, so the ones that are considered to sound as intended.
Ideally you would have both the mono box, recently reissued, and the Stereo Blue Box available secondhand. You might also want the German MMT and the analogue cut Red and Blue albums. That would be a nice sounding Beatles collection.
Discogs is better, there are sets on there for £300.
As I said above, I’d recommend both the BC-13 stereo and the Mono box, plus as Richard mentions, the German MMT is the best SQ of that album, & just about any Beatles album for me. They go for £40-50, usually.
As far as the qu about using a mono cartridge is concerned - didn’t Sean Magee in 2014 say that he cut the mono mothers with a stereo lathe because he knows it so well? (and also, I suspect, because a mono lathe wasn’t available or was knackered). Therefore, using slightly spurious logic, it shouldn’t matter if you replay using a stereo cartridge. Either way it sounds fab and is IMHO the only way to listen to the White Album for example. The only mono cart I ever tried was the Ortofon one and it sounded quite dull.
An update: A replacement box and copy of Rubber Soul have arrived - both look fine. However, the outer sleeve/wrapper for the box was not included I have asked UMUK whether this is coming separately, but then why would they not have included it with the box?
Given the imminent rerelease of the expanded Anthology TV series and albums I suspect there will be more related releases along soon. I have Mono on CD, nowadays ripped to my streamer, and they remain extraordinary recordings. Age and over familiarity doesn’t dim the impact of hearing them in mono again and being transported in an instant to the front room of my Nanna’s house watching the live broadcast of All You Need Is Love or hearing once again the extraordinary sound of all those Parlophone 45s I inherited. If you get the chance to buy in any format then you should.