Does the higher preamp gain result in a noiser background for the MC compared to the MM?
Unless the MC stage is a very good one, that is a possibility. The trade off is the greater responsiveness and subtlety of the lower output MC's vs. the higher output MM's and MC's.
Raul's point that MM's can be very satisfying is a good one, which he can make with authority since he owns more fine MC's than most of us own socks. Which type you'd enjoy more would depend on the kind of music you like and your sonic priorities. Since you're asking fairly basic questions, it's a fair bet you haven't fully expolored your sonic priorities, yet. Hearing different equipment types, if you can, is educational for both your audio brain and your ears. Educating them should be one of your higher priorities. Chasing different equipment without understanding your sonic goals can be fun, but it can also get very expensive.