The reason why you should use UPS instead of USPS is when you have larger packages as UPS is cheaper than USPS when shipping larger packages and is often faster than USPS.
Smaller packages are cheaper to ship through USPS though although packages can sometimes take a bit longer to reach the destination through USPS than UPS.
USPS is cheaper than UPS for small packages and UPS is often cheaper than USPS for larger packages.
If your package is large or is over 70 lbs then you should ship it through UPS or even FedEx but if it's a small package then you should ship it through USPS ground advantage if it fits the requirements.
The best way to mail a small package is to mail the small package through USPS ground advantage which is the cheapest option.
FedEx and UPS cost more to ship small packages so the USPS is best for small packages.
For shipping costs the USPS is the cheapest, especially for shipments of small packages.
I've shipped a small package that costs $15.60 to ship at FedEx and the same size package and same weight package cost only $7.10 to ship with USPS using USPS ground advantage.
UPS is often more expensive to ship with than FedEx and USPS.
Small packages are often better shipped using USPS ground advantage and larger packages are better shipped through UPS or FedEx.