I think it's because you know where the car is going to do when you are in the driver's seat, so you can mentally brace yourself and adjust your internal balance systems accordingly. Whereas, as a passenger, you have to react to the car instead of controlling it and so your internal balance systems are always slightly behind the actual motion, causing motion sickness. This is probably extendable to planes, trains, and busses.
If any of us ever figure out why, I'd love to know. It can get very difficult at times where I always have to drive and have to consider buses hard.