RD, I shipped the first gun I ever sold through UPS. That was about three years ago. It was such a PIA I swore I would never do it again. Since then I've shipped five or six guns through the Post Office with nary a problem (until this last one).
One of the guys in my hunting club ships a dozen parcels a week through UPS as part of his job. He told me they've had items damaged very very seldom, but have never succeeded in getting a damage claim paid.
I'm going to stick with the P.O. But you can bet I'll take good pictures of the gun before shipping and make sure I have good documentation.