For me, FedEx has been more reliable at not breaking things than UPS. We get deliveries from both on a daily basis and UPS is much more common to see a box that looks like it fell off the truck and then they backed up over it. Just for general reference (not that you asked), my rules of thumb for both though are:
1) Get an account and pre-print your own labels. No questions asked that way in my experience. I usually put a reference blurb about "kitchen supplies", "barbeque supplies", or "snowglobes" in case the question ever does come up.
2) Don't overpack. By that, I mean keep the weight and box size manageable. Much like overweight luggage on a plane, heavy and/or awkward boxes are never treated kindly by delivery persons.
3) Bag everything. I don't want anything to leak even if it breaks.