Obviously, in this instance Fed trumped Private. Now, I'm all for private enterprise. I'm all for workforce competition. And I'm all for results. There are things the private industry excel at doing, and there's things the state and federal governments excel at doing. I'm not, however, for any type of enterprise without proper oversight and review.
Now, I'm not sure why the US Army Corps of Engineers was not allowed to oversee levee construction for Lake Pontcherain and the canal system, but the New Orleans Levee Board has some serious questions to answer. Come to think of it, the USACE probably wasn't allowed since those things aren't US waterways, unlike the Hudson and Mississippi Rivers, although they did create Lake Texoma from several strategic dams along the Red River in between Texas and Oklhoma to prevent seasonal droughts and floods. For New Orleans, politics were probably involved since the other levees did deal with flood prevention.
Had the Mississippi levies failed, the French Quarter might be deflooded by now, if all the pumps worked and the breaches closed. That section would've sustained some gawdawful flooding, especially with upriver drainage. Katrina did track along the eastern side of the Mississippi, cutting NE around Ohio into Canada, dropping copious amounts of rain along the way. And all that water ends up in Old Miss.