I moved multiple safes at one point with a moving company, packed tightly with the firearms protected inside. The movers couldn't open the safes, and considering they were loaded on the nose with everything else in front of them, and the fact it took a forklift to get them in and out of the trucks, I was comfortable that the entire truck would have to be stolen before the moving company personnel would go through that trouble to OBVIOUSLY give someone access (or access themselves) to steal the safes.
I moved family from MN to TX in 1999, and the movers insist they didn't pack, move, or possess two revolvers and an old rifle which were packed inside of one of the dressers. We moved again since, meaning we unpacked, repacked, and unpacked again, and somehow have never found those firearms for which the moving company swears they never had custody... So no, I wouldn't trust any means of transportation where any individual firearm didn't come with the burden of weighing over 1,000lbs to grow legs.
In every move other than those two, I have personally transported all of my firearms. Planning one more move in my life, at least only one more where my firearms would be coming with me, I'll move them personally again.