Two UPS anecdotes:
1) Years ago I was hanging out at my favorite speedshop with my friends (the owners), and a UPS truck pulled up with varied car parts. One of them was an aftermarket fiberglass wing. The package (and subsequently the wing itself) had a round divet in it that looked very much like someone had stored it under a grand piano leg. And then stomped up and down on the piano. Of course the shop owners filed the "do not accept due to damage" form and the driver took it away.
2) I ordered a 22" Viewsonic P220F CRT monitor a while ago, back when they were "top of the line". When the UPS driver backed into my driveway and slid the box back to me, I eagerly went to grab it.... and noticed it was missing a corner. The box was missing an entire corner plus the styrofoam packing, a chunk about as big as a soccerball. The monitor itself was wrapped in plastic, but the corner was sticking out, and the screen itself in that corner was scratched several times. The driver looked at me and said, "Not going to accept it due to, I'm guessing?" Heh, yeah, no, didn't take it. Signed the electronic pad and he took it away. Another showed up a week later, this one the box still looked a little worn, but not like it had been dropped and clipped a shelf on the way down, and the monitor inside was new.
I've never had any issues with FedEx, DHL, or USPS, but those are just my anecdotes. Of the UPS and FedEx places I go to, the FedEx people are generally friendlier (a lot friendlier) but again, that's just my personal experiences with the two.