The Classe has the reputation of being the better performer for 2-channel music. The MC-1 has the reputation of being the best for HT audio. I have owned the MC-1 and the DC-1, but never have heard the Classe, so I can't offer a comparison. I will say that the MC-1 was much nicer on 2-channel audio than the DC-1 - much lower noise floor, much cleaner sound. Hockey is correct that the MC-1 digitizes everything, which is a limitation, but not a unique one.
I'm not sure about the comment that the Classe is a whole lot easier to use. Again, I've never used the Classe but the MC-1 is about as intuitive as I could imagine a unit being, but also has some very powerful configuration capabilities if you want to tinker.
Finally, if you want surround music derived from 2-channel sources, the MC-1 is very good in this mode as well. -Kirk