This conflates two very different things. Katrina was an example of the type of disaster that the federal government is specifically tasked with handling. And for most of the 90s, it was very good at handling them. But when George Bush became president and Joe Allbaugh became director of FEMA, everything changed. Allbaugh neither knew nor cared about disaster preparedness. For ideological reasons, FEMA was downsized and much of its work outsourced. When Allbaugh left after less than two years on the job, he was replaced by the hapless Michael Brown and the agency was downgraded and broken up yet again. By the time Katrina hit, the upper levels of FEMA were populated largely with political appointees with no disaster preparedness experience and the agency was simply not up to the job of dealing with a huge storm anymore.
The Deepwater Horizon explosion is almost the exact opposite. There is no federal expertise in capping oil blowouts. There is no federal agency tasked specifically with repairing broken well pipes. There is no expectation that the federal government should be able to respond instantly to a disaster like this. There never has been. For better or worse, it's simply not something that's ever been considered the responsibility of the federal government.
But there is one way in which they're similar. As Levin says, Katrina would have been an immense disaster no matter what. But it was far worse than it had to be because a conservative administration, one that fundamentally disdained the mechanics of government for ideological reasons, decided that FEMA wasn't very important. Likewise, the BP blowout was made more likely because that same administration decided that government regulation of private industry wasn't very important and turned the relevant agency into a joke. If you believe that government is the problem, not the solution, and if you actually run the country that way for eight years, it becomes a self-fulfilling prophecy. But we shouldn't pretend it's inevitable.
In the end, it all boils down to having competent people in government positions, not ideological cronies scratching their balls.