Still,. UPS is the best alternative. FedEx is also up there. USPS has lost/damaged more shipments than I can count to.
UPS did have an equivalent rival in the late 90s-early 2000s. Roadway Package Express, owned by the Roadway trucking company. RPS operated in the same markets as UPS and often matched them on rates/service. Apparently the Yellow-Roadway merger put an end to RPS. And DHL (which is owned by the German Post Office) attempted to compete with UPS in the domestic markets for a while - now DHL is mostly International shipments.
UPS has delivered almost perfect service, next is USPS.
FEDEX is the worst. 80-90% late, and 10% lost.