I used Pasport a few years back. I think Federal Express owns them now. Their enclosed shipping is as good as it gets. Here's an image of the car they shipped for me. The car is being dropped off in the image.
I've had opportunity to see a number of cars that were shipped using other shippers. In one example the car was scheduled to be shipped enclosed. They drove it up on an open trailer full of bugs and stone chips, saying, "oh we just switched the car in town to bring it here." In another example with another shipper they put the car on an open trailer and drove through wet white pait with the delivery truck. The car was sprayed with a mist of white paint. In another example the car above lost its transmission fluid on the hood of the car below. That was cute. In another example they loaded two cars one behind the other loose to have them rock back and forth with the bumpers hitting each other. There was plenty of damage. In another example the car was all thrashed up with dents on the top.