The signature electronics work with whatever you give it. On a long and short scale bass, the signal from the pickups will be different because the vibrating string will contain a different mix of fundamental and harmonic content therefore I would expect the output from the signature electronics will be different because it is receiving a different input signal.
if you could make both basses the same size, construction materials, pickup location and scale length, strings etc. then i would expect them to sound very similar.
I think in this scenario, the difference is more to do with the construction of the bass than the electronics. How significant the difference you can hear is would be up to your ears to tell you.
(Message edited by jazzyvee on July 14, 2015)