In some ways comparing MC and MM pickups is unfair. In general the top of the line MC pickups are way more costly than MM pickups.The question of which style is best is like a boxing match between a light weight and a heavy weight.
And then there are examples that don't fit the genral rules. I noticed that one writer said MCs have less moving mass than MMs. I suspect the decades old Technics EPC 100 MK4 MM has the least moving mass and you can find serious listeners who value it highly. And often the rare Decca pickups, not MC, are cited by people like Ken Kessler as the most dynamic pickups.
It's never straight forward. You need to know what kind of reproduction you like and look for a pickup that gives you that sound and whether it's a MM or MC should not be the deciding factor.
Oh and keep in mind that the phono stage you choose will have a big affect both on the sound and cost.