There is no real difference between MM and MC, the best of either genre are very very good - the worst of either... well lets not go there!
At the bottom end it is cheaper to make an MM than an MC - hence MM's dominate the cheapies.
Once you get over around $250 they are equal technologies.
There are fewer current manufacturers of true top end MM's but they do exist (Soundsmith, Audio Technica, Clearaudio, Ortofon, Grado...)
If you are planning on keeping things relatively economical - stay with MM - you will get better performance per $ both from the cartridge and from the phono stage, as both are easier and more economical to manufacture at that level.
High Output MC's have the advantage of using the more economical MM phono stages - not a bad thing!
For the most part, HOMC's are limited to the lower end and mid range of MC's - but Benz-Micro also makes some of their better MC's in HO versions... (Ebony H $3,500).
Getting the best from a high output cartridge (whether MM or MC) requires a phono stage designed for that purpose - many top end phono stages excel with (LO) MC but are only so-so with MM/HOMC. (making some of the comparison reviews a bit questionable...)
Final comment - getting MM fully optimised is in some ways more complicated, as it requires both capacitive and resistive loading, whereas MC's are mostly only resistive loading sensitive.
hope that helps
bye for now