I can't find http://www.bestratetransport.com - could it be Welcome to Best Rate Auto Transport
Transporters are pushing closed transport? Is open transport an issue? Is it any worse than driving the car 65mph?
I'd personally go for closed. Those trucks drive hundreds of miles through all sorts of environments with road debris to boot. Sure your car will be subject to some of that once you get it, but how's about you get it first?