I always thought that MC turtables were designed for the lower mv of the cartridges. If that is not true, :thmbsp:
I have heard it said that MC catridges sound better than MM cartridges but didn't want to take the chance of it not being capitable.
You tonearm is more important when it comes to MC cartridges - you'll generally want something medium mass and heavier to avoid compliance issues as MC cartridges are low-compliance. Low-compliance cartridge, high-mass tonearm. It's like a math formula!
As to whether they sound better than MM, that depends on one's tastes. My
opinion is that MC cartridges do
more things better than MM cartridges, and that's why they're often considered superior. However, there are still some things MM cartridges arguably do a bit better than MC. You have to also consider that MM cartridges only go up to around the $1000 mark, but MC cartridges can cost $15,000+, which, we'd hope, means a much higher performer.
In any case, your MH turntable should have a medium mass tonearm, which will absolutely work with many MC cartridges, especially if you add a headshell weight, but you don't have to. Consider, for example, the HOMC cartridge I use on my Pro-Ject, the Dynavector 10X5. It's an excellent match, and the next cartridge I get will also be a MC.