I prefer private, but also depends on the question. Sometimes people won't answer honestly if they know their answer is going to be seen by everyone, and will then go with the norm and vote the same way everyone else is (instead of by their own opinion).
If it's super personal or there might be a chance I'll select the controversial answer, I would like my response to be known only to me.
For example, questions about if you've cheated or have wanted to cheat. Sometimes it's nice to be able to be honest without worrying about a future or current significant other becoming upset if they happen to see your response.