We usually use Reliable (or I do it myself). They're usually a tad more expensive but we usually think its worth it for the amount of ins they carry and the way they treat cars.
I have a car restoration business so most of our clients are out of state. They've transported everything from 50k all the way up to 5 million for us and
we've never had one problem.
Others we've had scratches, dings, greasy hand prints on white interior, and one where they backed one car into another and when trying to work it out found out their ins had lapsed!
But it's mostly just using a reputable company so you can sleep soundly. Go with a company you've gotten recommendations for.