What is cheaper - UPS or USPS?

It depends on what you are shipping and how much of it (as in weight). You'd have to make a decision based on your shipping habits.

For most services the post office is cheaper. UPS does not offer anything comparable to first class mail. The post office priority mail (2-3 day service) offers fixed rates without weight limits or zones. Next day air prices (express mail) are comparable to UPS. The post office charges a small fee for tracking / delivery confirmation whereas with UPS it is free. The post office has free packaging for 4 sizes of priority mail. The post offices delivers to pretty much every address in the United States and has Saturday dropoff and delivery at no extra charge.

UPS does not have anything comparable to media mail. They don't have any way for you to ship (for example) 10 pounds of textbooks across the country for only about 4 dollars.

The post office is not a good place to ship large weights and very large packages. UPS is better equipped for that.