The privately owned tyranny has much less power, and when it becomes bad, government can intervene.
So while no tyranny is ok, government deserves much more attention, because it is the more powerful tool, that needs to be protected much more vigilantly.
Let's just agree that both can grow bad. It's just that clearly, governments+people can grow a LOT bigger (in absolute number of people) than a corporation, before it generally goes bad.
None of the largest corporations are really trustworthy, and neither are the largest countries stellar examples of good governing. The difference, however, is an order of magnitude more people being "managed". Apparently Google (Alphabet) employs about 100,000 people, most of them subjects not rulers. That's just a very small city or large town.
If we compare this to a small-medium sized country with a reasonably well-working economy, the difference becomes laughable: The corporation is a much, much, smaller group of people, with a disproportionally unwieldy huge amount of power, completely unable to control themselves and behave in an ethical manner. It's pathetic. YES they absolutely need a government to regulate them just like a baby needs someone to change their diapers.
I don't think it's so easy to separate the two. A corporation is not a real thing, it's a legal fiction created by a government. If a corporation acts badly, it's really the government that allowed it to act badly.
The complications occur when a corporation obtains enough power to be able to influence the government, and thus the ability to influence the rules by which it abides, like a recursive program which is able to alter the mechanics which created it.
At this point, the difference between government and corporations start to blur. It's entirely possible for a corporation to be initially created by a democracy at the will of the people, but over time, as its size and power grows, is able hold the government captive, and control its own rules.
Sadly, this is not just a hypothetical thought experiment.