Ask HN: Pros and cons of thinking in public vs. in private?

Dear HNers who engage in any form of "thinking in public" (whether that's blogging, posting notes online, or maybe even participating in HN/Twitter/forum discussions): What are some of the pros and cons of thinking in public vs thinking in private?

Since it's relatively easy to find the benefits of blogging and other ways of thinking in public, I'm especially curious to hear about some of the potential cons of thinking in public / the benefits of thinking in private?

And with that in mind, how does one effectively manage both to make the best out of both approaches?