The basic difference between them is that of leadership. The private exchanges will be run by local bodies, health plans and nonprofit organizations. The will feature health plans and premiums approved by the administering body. On the other hand, the state exchange will be handled by either the federal or the state government. These exchanges will be run according to the mandates of Obamacare act.
http://www.hcentive.com/private-health-insurance-exchange.html