Here is an example. Check out my country Atlas Shrugged. It has finance index of 190 and welfare index of 137. Highest levels on LU right now.
State corporation: Atlas Oil 001, total profit after all expenses paid by corporation is 1.17B.
CEO corporation (my CEO): Vandelay Oil 001, it pays 0.733B in country resources + 0.229B in taxes for a total of 0.962B. Then it pays an additional 0.55B in profit to the actual CEO, not to the country.
So here is the kicker. If the CEO corporation belongs to you, it is more profitable to build CEO corporations in your country because it will pay 1.51B in profit to you, but split between your CEO and country. However, if the CEO belongs to another player, you will only receive the money paid to the country (0.962B), which will be less than what your state corporation can make (1.17B). The main reason why it is less is because state corporations can run at a much lower salary and still maintain 100% hiring because you will have complete control of education levels. 200 is the optimal salary to maximize profit. Try doing that with a CEO and you will see your hiring will tank, whereas with a state corporation, you can manage 100% hiring at 200 salary by running your country well.
So in conclusion: max out ceo corporations from your own CEOs. That lets you build 20 + 20 ceo corps in each of your own countries. This will allow you to max out your disabled and housewives. Then just mass produce state corporations after.
All of these numbers assume fully upgraded corporations btw. When corporations are not upgraded, it is better to have CEO because they always pay country resources used regardless of profitability. But who has non-upgraded corps anyways right?
Oh and one last thing:
I have my tax rate at 30% and it is still better to have state corporations. A lot of players run 0% tax rate, which is completely illogical and actually makes the gap between state and ceo even wider. 0% countries are missing out on huge amounts of profits. I wouldn't recommend that for anyone. I don't even build CEO corps in 0% countries anymore because they are so flooded with corps that they can barely manage employment levels even at 300 salary, and I have no desire to decrease CEO profitability even more by raising salary to keep 100%. I actually build the majority of my corporations in C3 countries because since the C3 updates a few months ago, they actually maintain 100% hiring and welfare indexes well above 100.