A large part of my Family works for UPS, and I ship Fedex.... (Only because its closer to my house)
Really, all shipping companies are the same, if one broke / lost something of yours, and you switch, its only a matter of time. Like everyone else said, its a volume thing. They deliver around 5,000 packages in my city each day, if one get dammanged those are really good odds. If that one is your package, then you are very lucky :d.
Yes, a lot of claims are rejected do to packaging. I would guess that 80-90% of items shipped to not meet the packaging standards. If you really care, go to a UPS STORE, and pay the fee to have them package it.
Most UPS drivers are in this for the long haul, and keep the same routes, so make sure to get to know them.