It all depends on how the cartridge is voiced. The different types do have slightly different characteristics, but a MM can be really warm or very bright. The same holds true for other types of cartridges. Some are very neutral, while others are voiced to be more euphonic.
I prefer MC cartridges, as they do tend to present more details and have less "grain", however I'm currently enjoying my Soundsmith Aida II MI cartridge, which comes very close to the performance of my much more expensive MC cartridges.
Most MC carts require more gain due to lower output. They are not all "typically" .2mV. Many are in the .4 - 5mV range. There are high output MC cartridges that don't require as much gain (usually around 2.0 mV) and may work with a MM phono stage, but typically don't sound quite as good as their low output versions.
It's important to match the cartridge to your tonearm and phono stage. A well matched MM may sound better than a similarly priced MC if not matched well to the rest of your analog chain and your listening tastes.
In other words, MC, MI, MM is just one factor to consider when purchasing a cartridge.
