I have had problems from every shipping company, but UPS by far has had the best customer service for me.
I actually had a Fed Ex worker call my house at 4:30am one morning demanding to know where my house was. They were so rude, I had just gotten my baby to sleep, and my wife was having surgery the next day. Needless to say I gave that dude an earful he won't soon forget. I think all the Fed Ex drivers are scared of me now as a result. They just leave my packages tied up in a garbage bag tied around my mailbox (no damage yet, but when I do get one I am going nuts on em again). I ofcourse went up the chain of command and I think the guy was removed because they actually had it on tape! The tool didn't understand that some calls are taped to ensure good customer service.
The local post office I live near knows me by name too. I have even had insured parcels show up damaged they refused to give me the monies for because "the box was not packed well." It was full of bubble wrap and peanuts. I raised the roof there too. It probably wasn't the smartest move on my part as I have to continue to deal with them, but the service has improved a bit.
I usually just have stuff shipped to work as I usually get the best results there. I will admit that the last few packages that have come to my home have came pretty decent, well one box had the corner crushed.