Well, this is a good resource to start with: http://www.pisotones.com/BigMuffPi/psst/BMP_versions.htmMr. Hammer, what is the sonic difference between IC and normal transistor Muff??
The cardinal characteristics, and soul, if you will, of the BMP are the use of double clipping, and the mid-scoop introduced by the tone control.
All transistor versions share the same double-clipping, even though they may approach it slightly differently. The op-amp version has only one stage of diode clipping. Where it is also different is that it sticks a 2-pole lowpass filter ahead of the clipping stage. Using the filter means the signal is "rounded off" before it hits the clipping stage, which is a good thing. But having only one clipping stage, and especially given the higher clipping threshold adopted by means of a 3+3 diode compliment, means it should (in theory) be less compressed and "violin-ey" in its sustain than the transistor version. It also has a different scoop which appears to be both wider and situated a little higher up, more like a Russion.
I say this looking at the circuit, but never having heard one, so take it for what it's worth.