In almost every case, the shipping method, not the carrier is what matters. Opting for the free or least expensive shipping definitely is a major damage risk for oversize and overweight packages because they are in the system for longer periods waiting for similar or like shipments to consolidate. If the company you choose gives choices, pick the shortest timeline door to door and pay the price.
Experience is what you get when you don't get what you want.
"We'll be friends until we're old and senile,....then we'll be new friends."