This is somewhat of a generalization, because of the different eras of the Big Muff. But a Big Muff will have a lot more low end, scooped midrange, and a bit more gain. They are a bit more wooly sounding. MKIIs have a leaner, more focused fuzz tone with more of an emphasis on the midrange than a Fuzz Face or Muff, but still have a spitty, fuzzy decay with more theremin/synth like overtones with sustained notes.