Which is best depends very much on the mission you are trying accomplish. If you need to get something delivered overnight, Fedex is hard to beat, For 2-3 day service, UPS usually has better prices,and for ground transportation, if it is more than a 2-3 pounds, UPS wins every time.
For less than 3 pounds, you have to the math, at one pound USPS Priority mail wins, but after that it gets more complex.
If you are shipping outside the USA, it depends upon the destination. Fedex works very well in places that are friendly to the USA, and can be a disaster in places that aren't. For example if you want to ship to Saudi Arabia, and have it arrive on time, DHL. Fedex doesn't have a courier license into the Kingdom, and that causes massive delays this time of year (Ramadan). To unfriendly places, DHL wins hands down, although DHL is sometime referred to as
Documents hopelessly Lost, or Don't Have it, Left it.
The one bad apple in the whole bunch in Fedex ground/Home. Avoid those people like the plague. The only thing I ever get from them is headache.
International shiment by post usually doesn't get charge import duties or local taxes. Such shipments by UPS, DHL or Fedex always will, since they handle their own clearance, and usually charge like a wounded bull for the honor of doing so.