Never had a problem with UPS, but I did have to file an insurance claim with USPS, and I can tell you they they did pay to reframe my mothers pictures that were damaged. And it only took two weeks to process and they were NICE, funny, but then again it wasn't the local counter lady (she's got a rep)
Shipping I used to ship hasmat as part of my job, when I worked, and it can be a pain, mostly because nobody except "the guy" knows anything, and every once in while you run into somebody who thinks they know.
That being said, also worked with guy who used to work for shipping companies, and it's relative, however when I missed my delivery UPS was happy to send it back to the airport hub office, and two security screenings later and a stink eye (the box was a little banged up and it was a supervisor bringing it out to me, so he wanted to make sure nothing was damaged, I was like, um but you know, well ok) I walked out with my gun.