I say both...
About a year ago I was in exactly your situation. I wanted an adventure to go with my new (used) cobra, but I wasn't sure about trusting a used vehicle I had never seen, and didn't know anything about. I ended up hooking up a closed trailer to my dually, and with my 30 year old son as co-pilot, drove the 3500 mile round trip to pick up the car. (from Dallas, TX to Vintage Motorsports in CT)
We had a great time on the road trip, and some unforeseen issues along the way, but my car got home looking as marvelous as it did when I picked it up, and I didn't have to let any small town grease monkeys have their way with it along the way. We also enjoyed the fun of people questioning us about what was in the trailer at various gas stops, then dropping that rear door / ramp and listening to the ooos and ahhhs of amazed onlookers. Because we had the time, we even offloaded it a couple of times and let people hear the thunder and take pictures.
Turns out, the car would probably have made the trip without incident, but I preferred to take my trips on MY terms, and not rushing nervously in case of problems.
What - you DON'T have a dually and covered trailer?
Assuming you can't borrow one, a well maintained rental would do the trick...
Either way, enjoy the ride.
rs