I wish I had some kind of statistics or something to offer, because this is GQ, but all I can offer is personal testimony.
I have a friend who bought his girlfriend a brand new computer and shipped it via USPS. It arrived smashed. It looked as though it had been drop-kicked. The monitor glass was cracked and the computer would not even boot. Even though the package had been insured, it took them over 10 months to get their money back, and I am not positive on this point, but I don’t think they even got back the full worth of the computer.
I have heard nothing good or bad about UPS or FedEx. Personally I would feel better about moving a computer if it was packed in styrofoam and wrapped in a blanket in the back seat of my car.