I think the 2-band is quite different than the 3-band. Others can explain the technical reasons for it, but somehow the 2-band has a rounder, richer tone to my ears, not as reedy. Still sounds like a StingRay, though.
At the risk of boring the socks off anyone who's read any of my previous posts on the subject ;
I think the biggest perceived difference between the 2 band, and 3 band Stingrays, is due to the majority of people not really understanding how they work - and consequently, expecting comparable sounds with the knobs dialled in to the same positions.
The 3 band EQ was designed to sound the same as the 2 band version (with bass & treble turned up full), when the 3 band has the bass & treble up fully, but the mid left flat, in the centre detent.
The 3 band EQ offers cut & boost control, which means 50% of the pot's throw covers the boost range, and 50% throw covers cut.
The 2 band EQ is boost only, which means 100% of the pot's throw is dedicated to finer control over the level of boost added.
So when translating settings from a 2 band, to a 3 band, you can see there are several considerations, and limitations :
A 2 band with the bass pot set at about 30% is going to sound completely different to a 3 band with it's bass pot in the same physical position (which would actually equate to a 45% bass
cut).
Furthermore, there's the issue of matching the mid control. As mentioned, the 3 band with bass & treble at 100%, and mid in the centre detent (50%) position, sounds the same as the 2 band with bass & treble at 100%.
Conversely, the 2 band with bass & treble at 0%, has the same tone as the 3 band with bass, mid & treble in the 50% position.
There are some minor caveats, in that due to the way the filters are implemented in the 3 band, there is slightly less sub bass produced (and personally, I think there is a slight resonant peak around 2kHz-ish, due to the crossover, that can become obvious depending on the EQ settings), and the 2 band appears to have a low pass filter that is engaged with the treble pot at it's lowest settings (presumably to kill any high frequency noise).