Mozilla Persona, the former BrowserID, is still in the early stages. Once it reaches a more complete form, it could prove a solid and independent alternative to using Google or Facebook for simple logins. For now though, things are in flux.
API only comes with three functions, one for "watching" for login notifications from the service, one for requesting a login and one for requesting a logout.
Mozilla plans to upgrade Persona to the beta stage this September, at which time the Observer API will be the preferred one. But there are no plans to deprecate the older API yet.