Dan
Check the price.
Priority is a flat rate service ('if it fits in the package, it goes for the flat rate'), whereas first class is weight-based. What that means is that unless the package is very light, priority is likely to be less expensive. Also, priority in inherently trackable - there is an additional fee to track first class.
And the thing that USPS doesn't always tell you is that priority often gets to the destination faster.
Priority was designed as a package service (upgraded parcel post), and the USPS web site was designed to sell prepaid labels. The presumption on first class is that most folks will just stick a 'forever' stamp on the envelope.