A big government can also be corrupted by big corporations bigly too. Not at all clear there's a correlation there or which way there is. In fact there's more incentive and larger attack vector to corrupt a big and powerful government. It appears that is a separate matter entirely.
There is a big difference still. For a corporation to become rich and powerful in an anarchical environment as you describe, they have to provide good and services that people voluntarily choose to pay for, so they have to appease the people, or at least a large subset of them, directly to retain the power. For a big evil government that is not the case at all. Look at all the Communist/Socialist/Islamist disasters. They are impossible to vote out.
Corrupting a big government is much more expensive. Giving power from the government to the corporations just shifts the incentive from corrupting governments to corrupting other corporations. Want tariffs on goods you produce? Bribe a few top people from the biggest shipping companies (or even just buy that as a service, they'd probably sell it). I'd say that's much easier than corrupting a democratic government that has to be at least somewhat transparent in its decisions.
> so they have to appease the people, or at least a large subset of them, directly to retain the power.
The biggest corporations would not operate in an industry with a lot of competition, the biggest companies are the ones that can get a near monopoly on some good. Without a strong government to break up monopolies, it wouldn't matter what people think about the companies, they'd still have to buy. Even if that doesn't work, a simple rebranding and a purchase of a propaganda campaign from the biggest media corps will do the trick. Even if the corps in control change occasionally, the people behind them probably don't change as much. The same group of the wealthiest people would likely own many of the corps, so it wouldn't matter to them which one is in control, as they all serve their interests.
There is a big difference still. For a corporation to become rich and powerful in an anarchical environment as you describe, they have to provide good and services that people voluntarily choose to pay for, so they have to appease the people, or at least a large subset of them, directly to retain the power. For a big evil government that is not the case at all. Look at all the Communist/Socialist/Islamist disasters. They are impossible to vote out.