I had a pre-Vintage Circuit 4003 from 2005, and that sounded pretty full.
It's the VC that takes the guts out of the sound.
According to the Paul D. Boyer book:
"From the beginning of the Rickenbacker bass design, a 0.0047uF capacitor was wired into the circuit to cut bass response from the treble pickup, giving it a brighter sound. Simply replacing the capacitor with a piece of wire was the quick and easy fix. In 1984, RIC responded to customer preferences and jettisoned the capacitor, giving the 4003 a more ballsy sound right out of the box"
"Starting in early 2006, RIC restored the 0.0047uF bass cut capacitor to the circuitry. But a push/pull switch offers the option to activate it" (p64)