One place where the USPS will beat out UPS, FEDEX, or anyone else, is shipping overseas, especially to APO/FPO (military) addresses, where everyone else considers it to be "overseas", and charges outrageously higher rates!
I lived & worked on Guam (part of the USA for over 100 years now) for 7 years. I wanted to ship a 40 pound box to myself one time, from California. USPS Priority Mail cost me $44 + insurance. UPS wanted $175!! I think it just stinks that they rip off their customers that way, even tho you're shipping to part of the United States, just because they have to fly the package over the ocean (same as the post office does).
Just my 2-cents worth, but my buddy who's stationed in South Korea this Christmas will be getting a Priority Mail package.