I have had numerous BAD experiences with UPS when trying to make damage claims, but one very good experience with FedEx. They were friendly and very quick to reimburse me for the total amount I had insured the shipment for.
Of course, in my case, it was a $1100 laserdisc player, which was packed in its original packing material. They must have dropped the thing 20 feet. The stryrofoam underneath the player was compressed about an inch, and it landed so hard that the optical pickup inside actually *dented* the case outward.
So, anyway, in the event that you followed correct packing procedures (Which as far as I know, involve double-boxing your shipment, and seperating the 2 boxes by at least 2" of styrofoam peanuts on all sides) you will probably have a good experience. If you just put the PC in a box... dunno how that'll go.