There is really no comparison between these two knives. The BM's blade is made out of 6AL 4V titanium which is relatively weak while the MPF's blade is made up of Beta Ti which is considerably stronger and also a little harder due to more alloying.
The tensile strength is around 150 ksi for 6Al4V and around 240 ksi for beta ti. Rockwell hardness is higher for the beta, but both are still low. Edge holding on my MPF is comparable to the softer stainless steels like 440A etc. The BM has a thinner edge due to it's chisel grind so it gives the impression of lasting as long. It also has some sort of tunsten carbide coating on it that improves edge retention. These coatings are good for chisel ground blades since they remain right up to the edge on one side while you grind away the other during normal sharpening.
They are really two different classes of knives. The BM is designed for those who cannot afford to go to the MPF, and it is good at what it does. The MPF is just a step above.