I have pretty good experience with prime in San Antonio with both UPS and USPS. I can't remember the last time I received something from Amazon by FedEx.
In fact, the only time I get a package from USPS on a Sunday is when it's shipped Prime. I thought the delivery ETA was a system error the first time I saw a package estimated to arrive on a Sunday.
And that is with stuff coming from other states (I always hope for that to avoid the 8-9% sales tax markup.)