It's interesting that your link starts with the private companies Haliburton and Bektel loosing $25billion.
But apples to apples comparisons might make more sense. Perhaps governmental emplioyee IRS agents vs private subcontractors?
http://www.npr.org/templates/story/story.php?storyId=101558116
We could look at California's attempts at deregulating power, or we could look at private-owned prisons, or we could look at how efficiently companies like Haliburton move fuel in Iraq compared to the millitary doing the same.
Though I'd think we would do best to look at the other first-world western democracies. Every one has universal healthcare. Every one has cheaper healthcare than us. Most have better healthcare to boot.