Corporations have the same incentive as government for efficiency, albeit enforced by different mechanisms.
It's just that in some cases, in some parts of the economy, the mechanisms that regulate a private company are better. Most of all, this applies to sectors of the economy where the rules of the business can change rapidly, where you have multiple competitors in a situation where the customers are equipped to make a truly well-informed decision, and where the benefit of cooperation does not exceed the positive outcomes of competition. To me, the best example of this is the computing industry, and a comparison between the US and Soviet computer industries are profoundly striking.
Now, that does not apply for all things, just a large amount of them. And one rather extreme counter-example is a weather service, where you're basically dealing with - first, basic research, which never makes fiscal sense to MBAs and so long-run R&D departments tend to get cut quite severely when parent organizations are privatized. Secondly, it's data processing based on the maximum number of data collection points. It's called a "natural monopoly"; Essentially, you want a monopoly rather than three or four organizations competing with a third or a fourth of the sensor coverage, so the task is best executed by a monopoly.
Besides, the US Weather Service is really pretty excellent. Their ability to constantly improve their quality of output is striking, and they are masters of prediction.
Private companies are quite robust because they always have a bottom line they can steer by. If you're in the black, you're doing fine. Government institutions can really only steer by the expectations of the voters, and by constantly lowering them that inherently causes the government efficiency to drop - so it's a self-fulfilling prophecy. Expecting efficiency from the public sector really does work.
I'm a big fan of the private market, but the extent to which a lot of people oversimplify its strengths and ignore weaknesses is counterproductive. The world is full of nuances.