The ends of government are different too. Maximizing shareholder value, the supposed mantra of the business world, is somewhat complicated if your customers and your shareholders are the same people.
Finally, austerity in the business world is very different from austerity at the government level. In the business world your austerity measures primarily effect yourself and your employees. In government austerity impacts the customer base as well. I don't think there's anything about a CEO's job that would prepare them for that sort of thing any better than someone else. I mean, they're smart motivated and capable people for the most part, but that hardly separates them from the field of Ivy League lawyers normally in contention for these things.
The only people I can think of who are uniquely suited to leadership during a financial crisis are people with experience and understanding in macro economics. Maybe economists? Who else actually gets their heads around this stuff on a regular basis?