Private corps can upgrade higher than State and enjoy higher wages, the Ceo also pays for the corporations costs. The overall profits for the hoste are much greater than State. Disadvantage to Private corps is finding CEO's, control over corperation type (you can communicate your needs) and life of the CEO.
Public corps work the same as their former state, State or Private. The diferance is that shares are sold to foriegn investors, thus reducing the hostes overall profits. When over 75% of the shares have been sold, the Public corp can upgrade higher than Private. The advantage is mostly in the profits from selling the stock. Disadvantage is that the Public corp is vulnerable to hosile take over and doesn't produce much more profit than the State corp after your cut.