I've done both numerous times. I am a promponent of shipping the car if you have the money. Driving long distances yourself insures that you'll get some lovely chips and scratches, since you'll be driving over 55 mph for all of it. If you do drive, avoid driving during peak hours, morning and early evening near metropolitan areas.
To ship your car, I'd recommend Dependable Auto Shippers (DAS). They have a variety of options, but you are looking in the ballpark of $1,200 to ship a car cross country in an enclosed carrier, that is important always use an enclosed carrier.