Yes, private corps are generally better for your country than state corps.
The "income from enterprises" category in your P&L is substantially higher per corp than the "profit paid from state owned corporations" category.
More private corps also allows you to send more housewives to work, and rehabilitate citizens on disability. Both of these increase your employment index, reduce your social security costs, and I think they may also increase your welfare index.
There may be other benefits that I don't know about, but these are enough for me to want as many private corps as possible in my countries.