Hey El, they sound quite different is the short answer, as you know I've owned both and I still get to play through my old MP1 from time to time as MikeB has it. And also coz Mike and I are in a band together, I get to hear both at the same time (both cab simed and loud and live).
The biggest difference is (sound wise) probably in the voicing, MP2 has 10 tube voices (no SS) from clean through to very high gain. Some say the MP2 sounds too processed (well depends on the settings selected but I don't agree anyway). The MP2 is capable of a much wider variety of tones than the MP1 (well IMHO), and I've never got (or tried to get) the MP1 sound from my MP2. I like the MP2's sound. I also very much liked my MP1, served me well for many years/gigs, it's probably best described as a more "organic" tone than the MP2.
MP2s have lots more gain than MP1s (hence 3TMs, well to some extent), but also they have just about everything you need in them, if they had a decent stereo digital (or analogue (harder to do)) time based FX (delay, reverb etc), you wouldn't need anything else for recording, and live just power amp(s) and cabs.