I have a regular UPS driver, and as long as she's not on vacation, I never have any problems. Once I had a delivery of frozen rats. It was summer and I wasn't home when she came. She knew what was in the package, and didn't want it to set in the sun all day. She also knew where my wife worked at the time, a fact I would have never suspected she knew, so she took the package to her so she could keep it cool. Not many would go to that trouble. The substitute drivers however can be a nightmare.
I suspect that neither company is all that much better than the other overall. It's a matter of which is better or more reliable in a given area. Some people have particularly bad service from one or the other, but I find the service in my area is not tremendously different, both have decent records. I'm not prone to having problems with either one, but I have had more problems with UPS. They don't mess it up that often, but it seems when they do they mess it up good.