One major difference is that if you log in to a site with Facebook then Facebook knows you logged in to the site.

Whereas if you log in to a site with Persona, that's between you, your browser, and the site. Mozilla is not pinged with any details about you in the process.

Furthermore, Persona is decentralized. Anyone can run an identity server (though sites don't have to trust all servers, obviously). So you do not in fact have to build an account with anyone new if your mail server deploys Persona and sites trust it to identify people. The article points out the Yahoo has rolled this out already, so anyone with an @yahoo.com mail doesn't have to do any new account-building.