For Car Relocation the first thing to note is that most packers and movers company do not own any trailers. They book a space with the company which owns the car trailers at a fraction of the cost that they charge you. Incase they are not able to find space in a car trailer, they actually drive down your car to the nearest point (or in some cases the entire way) till they can find a trailer. Also since they don't own a trailer they cannot guarantee that your car will arrive safely.
The best thing to transfer a car is to find the company which own the trailers and ask them for a quote. Get your car loaded in front of you and pick it up where they arrive in your destination city.