UPS is union, actually, and not horrible. I think some of the elements of FedEx are as well (FedEx Ground is basically RPS via an acquisition, and their employees have universally sucked in my experience, but they're not union -- there's a push to unionize. I do believe FedEx pilots and maybe some other parts of the air operations are union.)

I don't think USPS is that inefficient for some of its operations.

FedEx (Air/Express) is the gold standard for premium delivery.