If the item you're shipping will fit in a flat rate shipping box through the USPS then the USPS flat rate shipping would be the cheapest to ship the item especially if the item is a bit on the heavy side as long as the box can handle the weight without coming apart and as long as you can seal the top of the box without it bulging.
If you can't ship the item in a flat rate shipping box then the UPS would be much cheaper to ship the package with.