First off, they were extremely easy to fit. I've dealt with some stubborn Michelin tyres meant for road riding and cursed the puffy man on the package at every step of the process for my aching thumbs, but the Muds went on without a fuss, and not the kind of lack-of-fuss where you think something must be wrong. As long as you make sure they're facing the right direction (they are directional tyres) you'll have an easy time mounting these tyres up.
I can't really compare tread patterns between the new and old Muds because I've never ridden the old ones, but I can say that the Mud 2's appear to have a more aggressive directionality to them and a generally rounder profile on the rim. While the original Muds were composed of blocky trapezoids and steep side-knobs with a very shallow angle, the Mud 2's have a staggered pattern of knobs with more frequent spines. In essence, it's a lot easier to tell which way is forward with one of the new Mud II tyres.
So what conditions should these tyres even be used in? Michelin tries to steer consumers in the right direction with the name of the tyre I suppose, but I found it to be surprisingly efficient beyond that. The spines and directional pattern mean that mud is shed very efficiently, but the directionality also means that the tyres can keep you moving pretty quick. At no point was I wishing that I had a tyre with less tread on it, though perhaps that was the nature of the Cross courses I was riding. While I didn't try many very technical sections, I also didn't have many if any moments where I was missing grip, aside from the odd damp log here or there.
In the end, the Mud 2's may have been my favorite CX tyres I've ever used so far. Not just for how surprisingly capable they were outside of their comfort zone, but for how versatile they were. For me, the extra hassle in rigging them up tubeless was definitely worth it for the versatility and reliability of the Mud 2's.