In the days when The Beatles first recorded, stereo was a brand new idea. Almost everyone had a record player that played in mono. So when they had the recordings made, they had to fit in all the sounds they wanted to be heard into one track. That was a very difficult operation, and took many hours of combining different tracks and then combining that result into other tracks. The result was a super master recording that contained the hole song coming from one speaker.
Then someone said "Hey, there's this new thing called stereo, why don't you mix your albums for that too?" So, starting with their fifth album, they did all the work I described above, and then went back and did the same thing again, but in stereo = two tracks. But since it was a new technology, they spent a lot less time on it. And they really didn't worry about making sure it was perfect. They probably guessed nobody would listen to it anyway, so they did a pretty good, but not "perfect" job.
Over the years more and more people got stereo systems, and the people who listened for details heard many, many differences in the two mixes. Some songs a re slightly longer or shorter. Some have different points where instruments come in or out, and things like that.
The difference between the two box sets is not just that one is stereo and one is mono. These are two VERY DIFFERENT mixes of the same songs. For the die-hard fans of the group, it's like hearing the songs all over again for the first time.
