Both schematics are, from C3 to the output, functionally the same. To change how the bass sounds when the treble control is fully open, use a 250K VR3 for a vintage one with less treble, and a 500K VR3 if you want a modern tone with more zing.
C3 is probably there to give a bit more growl to the tone (a lower resonant frequency) even with VR3 fully open, and R1 gives it a generally brighter tone with more resonance (a higher peak). As for the SW1/C2 combination, that gives the series mode slightly less muddiness.
Squier VM Bass VI club member #19