Many more users are going to have Facebook logins already, and it provides social information that may be useful to your app.
(Hoping to hear answers other than the dev-centric 'I don't like facebook')
You can additionally just ask for the users email address.
Any one building a serious business using facebook auth does one of the above.
us3r-1D@facebook.com - that's helpful :)
I'm simply not trusting facebook under any circumstances. I'm in the minority, I know. But, if you want my money, or my time, on your web app (and maybe you don't; maybe you want people who have low desire for privacy or security, since they're probably more likely to click on ads), you're gonna have to offer something other than facebook for logging in.
Often the comments we want to write on websites have absolutely no business being concurrently posted back to FB. People like contributing without disclosing or offering their FB identities or sharing every micro-activity. And fair enough.
Not everyone is comfortable with fronting up to an unfamiliar website and saying "hi, I'm John Smith. Here's my comment about religious persecution in South Asia. And don't forget to Like me on Facebook. Sign up now to connect and share with the people in you life"...
In other words, the less clunky FB social plugin mess on websites the better. I hope Persona goes well.
You should use both, to maximize the convenience of your users.
Some are always signed into Facebook, and like to just use that, others want other methods that offer different models of security and openness, Persona is the best of those I would argue (OpenID is nice too, but the lack of native browser integration is what makes it less impressive than Persona).
There's more to Persona than liberating you from your password column.
Nevertheless, there are still huge classes of applications that don't benefit from social features, but do want the improved experience that Persona can offer. Think banks, universities, corporations, and governments.
So even in the absolute worst case versus Facebook Connect, we still have enormous potential for alleviating the pain of per-site passwords and containing the damage from security breaches in day to day life.