I can't stop thinking about this one! The public me is much more cheerful and optimistic than the private me. The public me puts her ideas out there, while the private me worries they're not good enough. The public me says, "Hey, what's the worst that can happen?" and the private me answers, "How long do you have? I have an extensive list." There, at least, I find a bit of common ground. Publicly and privately, I love long lists.
How about you? Are there any differences between your public and private selves?