Bitcoin sought to reduce dependence on trusted third parties, where as, persona is increasing the reach of trusted third parties.  The keys and passwords are stored on mozilla's servers, sometimes on your email providers.  Persona, is however, a progression and will hopefully improve its security and decentralization as it goes along.

When Persona is supported by all the key players in a transaction Mozilla doesn't get anything, do they? You can easily run your own IDP on a personal server if you're the kind of person who likes to do that, then run Firefox so you have a native implementation and the Mozilla servers aren't involved. The keys never leave your computers.

Whilst X.509 certs can indeed be issued for any arbitrary string, you still need a CA that will do it for you, and that's typically not so trivial. CAs aren't meant for widespread end user adoption, really, whereas Persona is.

I don't think Persona is any more or less centralised than other PKIs, really, just easier to use. Ultimately the string you're verifying is a user@host pair, so the host is centralised via DNS and to verify the assertions it vends, you must use SSL to connect to it, so under the hood the regular SSL PKI is still there.