I don’t know about the differences in the circuits and the stages, but:

version 1 has a rate knob, a blend knob (which I assume controls the ratio of the dry and effected signals), and a color switch (which I assume switches between 2 fixed values of feedback, like the small stone).

version 3 has a rate knob, feedback knob (which might as well have been a 2 way switch, because it’s really tough to distinguish any continuous difference from about 0 -75%), and a manual knob that allows you to replace the rate knob and control your own oscillation.

The Color switch on the v1 Bad Stone — the weird mummy face one — switches between a pitch shift vibrato and more of a chorus setting a bit like a leslie or a vibe. A lot of early phasers used that sort of terminology — my old Jen Motorphaser specifically calls them Tremolo (which is fast, like a Leslie) and Chorus (which is slow, like a vibe).
The later one with 3 knobs has a manual mode so you don’t use the LFO but set the phase shift manually with no sweep.

Here’s some samples of the early one (although this isn’t really a v1 Bad Stone — it’s a different circuit v2 maybe?): http://www.home-wrecker.com/badstone.html
And the later one: http://www.pedalarea.com/phasers.htm

The Bad Stone is an awesome phaser and was the first with feedback.

It’s not really a fixed rate, my bad description. It’s more of a Doppler pitch shift vibrato like you’d get with a leslie on fast speed, and a more chorusy sound like a vibe on slow speed, but you can still vary the rate of the sweep with the pot. Just think of it like a switch between pitch shift vibrato and regular phaser. Hard to describe, but it sounds great.