Comment My own UPS experience, plus valuable contact info (Score 4, Informative) 1554
I had similar problems shipping a recording console with UPS. They refused to even return my calls until I started threatening a lawsuit. I have made the entire story, including photos and contact information, available at http://www.christopherpetro.com/ups
As for FedEx, I have sometimes had problems with them (though far less often). The important difference, however, is that it has never required a threat of a lawsuit to get FedEx to cover my damaged or lost packages.