Having browsed through the set, there are some differences that I note.
The covers are different. It looks almost like the foil covers like the Core Rule set gift set had. I don't think that this cover will be on the general release for Monsters of the Multiverse, as I think the foil type cover was only on the Gift sets.
The Demonlords and Arch Devils...once again...have slightly different stats. The ones from OotA are still the strongest ones from what I see, but the HP totals in MotM have been pumped up slightly (so, in between MtoF and OotA).
Races have not ability bonuses anymore. It is all add +2 to one score and +1 to another. Alternatively, they can add +1 to any 3 ability scores. In my opinion, this inherently weakens humans as choice for race these days. They have a bunch of other abilities they can get as they desire. Lots of choices of races, including ones which I think only appeared in web supplements previously.
I like having so many Monsters in one book.
It really is basically races and monsters and nothing else. You lose everything else that was from Volo's and Mordekainen's if you only have this book. It's a great DM resource still, not sure if I would open the races up to PC's though. Maybe on a more limited basis.