The one I built was a clone of the Arbiter
http://fuzzcentral.ssguitar.com/fuzzface.php . Went the whole hog and bought replica single sided boards, carbon composition resistors etc.
The fuzz characteristic is that as the control is advanced, the signal soft clips asymmetricaly - kind of a half-wave rectified appearance. As the control is advanced it progressively clips on the positive and negative transitions. But it also depends on the drive level from the guitar. For a circuit with two transistors, four resistors, three caps and two pots you can get a whole range of effects.
Of course people analyse the thing, including spice modelling
https://www.electrosmash.com/fuzz-face . Although the AC128 spice models are not correct, the waveforms are pretty close to what I measured using a signal generator for the input.
The key thing with this little circuit is that the collector of the second transistor should sit at about 50% of the rail (9V battery so about 4.5V), but anything between 30% and 70% of rail should work OK. Tweaking collector resistors to achieve that might be necessary for particular values of beta that you have. In fact some clones have a pot in the collector of the second transistor to set the bias conditions
http://fuzzcentral.ssguitar.com/fuzz...facelayout.png
Craig