Passport control can be hit and miss because there are loads of charters which can arrive at weird times. If you're stuck behind one of them it can be long, but most of the time you'll be through quickly. Passport control is Swiss or French police at random (depending on rotas I guess), it's the exits after luggage carousels which decides where you exit. It mattered for duty free when the UK was still in the EU but now not so much. They're really walled off, the only way to cross from France to Switzerland is at the border control point in departures (it's rarely manned, but officially it's a border post).

For cars you've read it all above. The one advantage of Avis on the Swiss side is that your car will have the vignette. Taking cars across borders within the EEA shouldn't attract a extra charge. I've had Avis reimburse me the charge for admitting I was going from Slovenia to Austria, the guy wasn't going to let me have the car if I didn't pay. It's a single market, Avis corporate reimbursed it without question at the first email. Check opening times as well, I remember the desk on the French side closing earlier.