What is the difference between state and private exchange?

Nobody knows????

http://www.hhs.gov/opa/affordable-care-act/index.html

By private companies you mean several insurance companies got togeter and opened a sales website themselves? If so, then the difference would be that only the government site is going to offer the tax subsidies and/or cost sharing. If you want to pay for the insurance all on your own or make more than 400% of the Federal Poverty Limit, it would not matter where you shop (as you would not qualify for any financial help). Several states did open their own sites instead of using the Federal one and there is not much of a difference there. Except maybe that the state exchanges are running a little better than the Federal.