Now that I've upped my online guitar community cred by getting a sweet vintage Rat, I'm in the process of building a clone of a ThorpyFX Fallout Cloud, which is basically a more flexible Big Muff.
I love fuzz, but not just straight-up into a clean amp. I like using it in conjunction with high gain (i.e. putting a fuzz pedal in the front of a high gain amp, but with low fuzz settings, almost like an overdrive) in order to get a thicker, more lo-fi tone for certain textures.
This is all well and good but most fuzzes (Big Muffs especially) can't do this because they're so bassy and scooped. It just makes your amp shit the bed. You have to run an EQ after, or before, or run an OD in line with it or something.
The Fallout Cloud has bass and treble controls on it, and it's altogether smoother and more amp-friendly than a classic fuzz. You can really dial it in for your set-up, and it enables you to get all kinds of fuzz tones, not just Big Muff types.