It's not that simple. "It's him/her or me" doesn't cover it.
Optimally, it would be a partnership. This usually happens when a band has the same person running FOH every show.
This usually turns into a pissing contest here at TB. That's a terrible (and immature) way to go about it. "I've spent thousands of dollars and years coming up with MY SOUND and he better damn well put MY SOUND in the PA!!!" Never mind that the sound guy will ultimately win that battle every time. Why? Because you have to go back to the stage and go to work at some point. The sound guy is left there at the board to do whatever he/she wants with your sound. You simply can't win if you choose to lock horns.
Having run sound some as well as being a bass player, I can't tell you how much easier it is to really make you shine if you send me everything. What I mean by this is if you send me the entire frequency spectrum, I can mold it into whatever.
Over simplified explanation alert!
If your sound is too bright, with too little lows, I can boost the lows and beef up your tone.
HOWEVER, if you send me too much lows, and not enough mids and/or highs, I can't do a thing to clean you up and help you cut.
What generally happens is that bass players find their favorite BEDROOM tone after years of experimentation. They get to the gig and assume that "Any good sound guy will make MY SOUND work. Screw that guy if he doesn't like it."
I usually.... kindly and patiently.... try ONCE to ask for a little more mids and highs. If the bass player shoves that down my throat, I simply amplify their awful sound. You see, Jamerson's tone almost never works in a practical live situation. Sure, if you're playing in a Motown band, with stellar musicians who know how to create space for everyone like the Funk Brothers could, you'll be fine. But if you try modern country, rock, funk, stacked soul (wall of sound), etc. with a Jamerson tone, I can't do a thing for you. You're getting buried unless I knock down everything else in the mix with YOUR SOUND.
Short version: Your bedroom tone might SUCK in a live mix. If you want it to suck LOUD, be stubborn with the sound guy. If you want your playing to shine through, send as flat of a signal as you can live with to the board so the sound guy can do whatever is needed with it.