The question never is and never has been "public vs private"; rather, it is always does THAT SPECIFIC JOB match your needs, goals and personal style? I've worked at both and probably will continue doing so (currently, its private).
Two other comments: (1) I've found that the size of the organization has more bearing on the style than whether its private or public. Large organizations are almost always fairly bureaucratic, smaller ones tend to be much more familiar and dynamic (and riskier to work for) (2) I find the stereotype of lazy/incompetent public sector employees very misleading: there are idiots, a**holes, and various types of difficult people everywhere. Identify them, and avoid (or quit, if they are your boss or otherwise unavoidable/unbearable)