I have been through more cartridges than I can remember: MM, MC, MI, and I keep coming back to MC.
For my ears, MC has better detail, better attack/decay, creates a bigger better defined soundstage, better defined images within that soundstage.
I hear more air around instruments with MC. And I have found that MC tend to track a bit better, but they are also more finicky to set up correctly.
MC cartridges have a lower moving mass than MM cartridges, which accounts for most of the attributes that I like over MM.
When MC cartridges first started gaining popularity, there was an issue with bass being a bit lighter than MM, but that is in the past.
MM has an edge at the lower-middle price range. A $500 dollar MM has a good chance at outperforming a $500 MC.