There is a big difference; A corporation in the free market run like the government would go out of business.Imagine if you could vote with your tax dollars as you vote in the free market by purchasing things you want. Ignore the Galbraith view that corporations can trick people into demand with advertising. I've never owned an Apple product, "smart" phone, and new Coke should have been the most successful product in history. Everyone preferred classic Coke and voted with their dollars regardless of one of the most expensive advertising campaigns.
How many people in the Army Corps of Engineers lost their job over Katrina? A private business running the levies would have been held responsible for the deaths and probably would have gone out of business just over the fact they provided an inferior service and other clients would have cancelled their contracts. Also, any project as big as managing the levies would naturally demand the private company to have insurance to cover losses. That insurance company, being on the hook for potentially billions, would hire their own engineers to ensure the integrity of the system and increase premiums or drop coverage based on their own evaluation. Government regulators have no incentive to be effective regulators, they have an incentive to be ineffective because they are "captured" by the corporations based on the prospect of a high paying job in compliance when they leave.