Can someone help me understand the pros and cons of public vs. private unions?

I lived in WI for a long time, and a lot of my buddies are out there protesting. Before this, I never really considered any distinction between unions, but this issue has caused me to notice differences. I’d like to know more, so please describe the good and bad points of both, putting them in a historical context if you wish.

Please do not just take one side. If you describe the negative points, also describe the positive. Otherwise I may get the impression the info you are giving me is biased and not informed about both sides.