Which shipping option is better for books, UPS or USPS?

I have a dozen or so books that I’d like to ship across country. They’re heavy for their size, so shipment by volume rather than by weight would probably work for me—unless media mail (postal mail for books) is cheaper.

Am I right that rates for UPS go by volume and for USPS by weight?

I don’t need links to USPS and UPS, thanks. I’m just asking if someone has done a direct comparison and knows the answer already.