Low output vs. high output cartridges

Absolutely, The problem for high output MC's is that they have to have many more windings to generate the high output. This greatly increases even doubles the effective mass of the moving system of the cartridge. This is bad on several levels. The first is that the cartridge is not going to track as well. Second is that increasing the mass lowers the resonance frequency of the cartridge frequently down into the upper audio range giving these cartridges a shrill character. This can be partially negated by stiffening the suspension at the risk of tracking ability. In this sort of device the key to high performance is the lowest effective mass which is one of the reasons these cartridges are more expensive. The materials to do this are exotic and expensive. Some of them are difficult to machine, etc. This is the reason so many prefer the ultra low output MCs but for most Phono amps that is a step too far. 

Lewm, many people do prefer MI designs. They are uniformly great trackers. As for their sound, as you imply that is a matter of personal taste. The Grado Statement is certainly up there with the best MC cartridges. MM cartridges can also have pretty low effective masses now with smaller rare earth magnets, ultra small diamonds and boron cantilevers. Listen to a Clearaudio Charisma when you get the chance.
But, in comparing low to high output moving coils there is no comparison.
I would go with a good MM cartridge before a high output MC.
One more thing, the differences in effective mass between the best MI, MM and MC cartridges is not that great. The generator be it coils, irons or magnets is right on top of the fulcrum and contributes less to the effective mass of the cartridges moving system than the diamond and cantilever which are way out in left field.