Syncing comments between Facebook and Wordpress
This question is a bit old, but I actually got here from the official Facebook comments plugin page so I'm answering.
There is a plugin called WP-FB Comments
It's working fine, you can read my experience with it on my blog(currently trying out Livefyre so you wont see it in action)
I'm working on a similar 2-way sync project. There isn't a way to sync comments (at least none that I can find). The way this has been accomplished is to create a new Facebook application and thus you comment thru the app, not Facebook's native comments, e.g. WPbook. Obviously, it's not ideal.
Wordbooker is another plugin that can accomplish what you're looking for -- when someone posts on Facebook, the comment is imported into Wordpress, and when someone comments on Wordpress, the comment is exported to the Facebook post too. The developer is fairly responsive if you have any issues setting it up.