I took mine from Little Rock to Vegas on one and now my windshield looks like it was sandblasted (I believe a new one is $936.00...which is more than it would have cost to have it hauled there in an enclosed trailer..HINT HINT!), and the front bumper cover took a good bit of rock chips too. The crappy straps that go over the front tires kept slipping off, and pulling it through traffic played hell on my nerves. I'll never do it again unless I buy an enclosed trailer first; it's just not worth trying to save a few bucks. IF you DO go with the U-Haul, cover the windshield, mirrors and bumper cover with painters tape and bring a few extra rolls. Also, check the straps every 50-100 miles unless you want a lawsuit because your car bounced off the trailer and someone ran into it. Bring your own tie-down straps, and remember that there's no such thing as too many.
Call one of the guys on here that do it for a living and save yourself a lot of money and stress. I did it when I went from Vegas to Abilene, and I can't put a price on the piece of mind I had NOT having a car behind me. It was insured, and it arrived exactly as when it got on the trailer; I can't recommend this enough!