I've always used USPS, mostly USPS Priority 2-3 day shipping with insurance. Most of the time it reaches in 2 days, and 100% of the time it's significantly cheaper than UPS or FedEx. I've never had any delivery issues with them either.
What gives? I don't get it.
This may be true for light weight packages, or seriously heavy ones (using the USPS flat rate boxes), but for anything over ~8-10 pounds, the other carriers are less expensive, in my experience.
Last Christmas, when shipping out boxes, I went online and priced out all 3 carriers. It wasn't unusual for Fedex to cost (for instance) $15, UPS $18, and the Post Office $30, for the same box. And to the locations I was shipping to, Fedex could get it there in 2-3 days, same as the PO.
In fact, the only time the PO has been cheaper, for me, has been when I ship packages to my niece, in Japan.