That's a good article. You can hear the difference between the different methods.
The Bass Octave Deluxe does a bit more to deliberately change the tone on the Girth. If you look at R51 (330k) the V0.1 schematic it's a high value. That means when the JFET (Q10) is off the gain is about 1 but when the JFET is on the gain is about 7. So one part of the waveform gets stretched and clipped, which changes the character of the tone.
If you look at the schematic for the "other" "MXR Bass Octave" (I'm not actually sure what MXR pedal that is yet), you can see the same 330k as the Girth channel. The filter is different.
viewtopic.php?f=1&t=28143However, it is possible to make the MXR Bass Octave Deluxe with the 3x68k resistors sound the same as the filter in this circuit. Using the same sounding filter is a guess as without sound samples we still don't know if the Octave sound of the "MXR Bass Octave" is the same as the Girth sound on the Bass Octave Deluxe. It would be a good start though. Really, we don't know the Growl filter on the Bass Octave Deluxe is the same as the Boss OC-2 that's really just a good guess too.