I cross often and am never stopped by car. However on the train they always check passports. Interestingly at the train station in Geneva they just wave through blue US passports. They only want to look at the EU passports for some reason.

When I drive across they never ask for passports. If I cross by an autoroute they want to see the Vignette. But when I cross at small highway checkpoints they don't ask. I have driven through Switzerland many times with French Avis and Hertz rentals and never had a problem. But when I use my own car I make sure to purchase the vignette.