Have done both. The cost comes out to about the same cross-country, assuming you don't need your car for a week or two while it's in transit or you are able to take a week off to do the drive. If you do fly and ship the car, the cost of a rental will be a problem if you need one in the meantime.

I would make sure you have roadside assistance (AAA or otherwise) and keep your wits about you at truck stops, but otherwise it's just around a week's worth of driving if you don't want to burn yourself out. Lot of driving through forests, then plains, then deserts, so bring a couple of podcasts or something to listen to.