I ship a ton of stuff where I work. Parcel and freight LTL. In past years, it was generally regarded that UPS was rougher with packages than FedEx and DHL, but that has really leveled off. They're all terrible. The problem that we encounter where I work is that manufacturers have cost cut the easiest thing to eliminate, packaging. Cardboard is thinner and easier to tear and dent and packing foam has in most cases been eliminated completely, causing items to be damaged inside unopen boxes from all carriers.
BTW, the issues we're having with freight carriers is re-palletization. Manufacturers strap and palletize items, give that pallet to a freight carrier who proceeds to cut the strapping and shrink wrap and re-organize the pallet to suit their needs on the truck. This is usually so they can stack the pallet on other pallets for long distance haul. Weekly we end up having issues with missing items on packing lists and damaged items.
BTW, stickers that say "This side up" have absolutely no meaning anymore.