I never use onboard tone and volume; Got a multi-effects (Zoom B2.1) with tone shaping and a volume (among other things) pedal. So I yank out all the extraneous passive components from my basses.
Others have said that removing a 250K shunt to ground has little effect, but the fact is if there are multiple controls, they act as parallel resistances and can make a huge difference: 4 (2 tone and 2 volume) 250K pots in parallel acts as a 31.25K shunt. Removing one pot raises the resistance to 62.5K, removing two raises it to 125K and so on. Add to that the removal of the tone caps, and it can make for a big change in tone and output.
I notice a huge difference, much brighter tone, after wiring the pickups directly to the jack. If I need to change volume or tone, that's what my stomp-box is for, (and my feet are less occupied than my hands, anyway.) Let's face it, the onboard volume and tone controls are pretty primitive circuits, so all in all, I'd much rather use the more sophisticated ciruitry in my pedal. My next project is stripping the passive parts from my Ibanez 5-string, leaving just the PhatII tone boost. I'm also going to pull out the battery and supply it using a three conductor cable back to my pedal, taking the power directly from my pedal's AC adapter (a beefy 3rd party 1A 9V supply.) No more changing batteries!