Moving magnet carts have pretty big coils in them to pick up the impulses from the vibrating magnets in the cantilever. Since in a MC cart it is the coils that vibrate, those coils are smaller to assure enough compliance to track the record. Smaller coils of course will create less current.
Another drawback: Since the coils are connected to the cantilever, the stylus is not user replaceable because of the delicate alignment between all parts concerned. Additionally, most MC carts I've seen also require heavier tracking pressure- probably a necessity due to the mass of those coils and the tracking requirements of the stylus/groove (my theory...).
MC are supposedly better performers, but as for me personally, I just can't justify the expense.