Warning... uneducated reply coming!
As far as I know, Vmo and Mmo are not related at all. Vmo is a speed above which there's a danger of the aircraft breaking up due to the dynamic pressure forces and associated stresses. Mmo is a speed above which there's a danger of the aircraft breaking up due to the shockwaves on the wings. So, where you say that "they have the same Vmo limits", I'm not sure that's relevant.
Also, I don't see how the weight of the aircraft would affect Mmo. It may well affect Vmo, since the wings will have to provide more lift, and will therefore be subject to more force in all stages of flight. But the mass of the aircraft wouldn't affect the shockwave formation.
I'd have thought shockwave formation would depend mainly on the shape of the wing. So if the two aircraft have the same wing, then the only reason I can think of for the different Mmo would be the shape of the aircraft as a whole affecting the airflow over the wing, presumably giving a lower local airspeed over those parts of the wing where shockwaves are most critical.
But, like I said, this is largely guess-work. Will be interesting to hear from someone who actually knows!
FFF
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