Arguments: offline or online?

I saw a talk by JT Eberhard, and he said that whenever someone invites him to discuss the fate of his immortal soul over a cup of coffee, he agrees on the condition that the discussion can be put online.  This put on my mind the question of whether it is best to argue in public or private.  "Maybe I should blog about that," I said to my notepad.  And then Greta Christina blogged about it instead.

In a private debate, you only have a chance at persuading one person. In a public one, you have a chance at persuading dozens, or hundreds, or thousands, depending on how big a forum you have.
...
People may be ashamed to express stupid ideas in public — but once they’ve done so, they’re likely to get even more entrenched in them. Once we’ve made an assertion in public, it’s harder to walk it back. It shouldn’t be, but it is.

Noooooo!  Now that everyone on the atheowebs is talking about it, how can I possibly hope to contribute anything worthwhile?  It is the curse of blogs everywhere.

I don't like the way the choices are presented:  Either have a private argument over coffee, or have a public argument over coffee.  I simply don't have arguments over coffee.  I don't like one-on-one arguments, or coffee.  And opportunities for arguments over coffee never appear.  In my circumstances, this is the more realistic set of choices:

1. Talk about atheism without any provocation.
2. Talk about atheism with the slightest provocation.
3. Talk about atheism online.
4. A combination of some, all, or none of the above.

When I talk online, the fact that it's public is not the biggest difference.   The biggest difference is that I produce my own opportunities instead of waiting for them.  The second biggest difference is that it's in writing, not spoken word (where I am far less articulate).  The third biggest difference is that, since my preferred medium is blogging, I decide the focus, and argue with no one in particular.

Is arguing publicly more effective?  Among my choices, in my circumstances, it is definitely the most effective at, well, everything.  It's more satisfying to you, more satisfying to me, more likely to persuade people, and has a more positive effect on my relationships. But it's so tangled up in other inseparable issues, it's hard to say that it has much to do with the public/private aspect.