Brad DeLong gets the distinction between Friedman and Hayek pretty much right in my view.
I think that there is an important difference between Friedman and Hayek. Hayek is an economic (classical) liberal but a social conservative: a believer in respect for throne and altar. Social conservative Hayek can see Pinochet as a good thing: far better to have an authoritarian state that maintains the conservative moral order, if it can be persuaded to adopt laissez-faire economics, than it is to have a democracy that regulates the economy. Friedman, by contrast, hates and fears a government that prohibits use of recreational drugs in your home almost as much as he hates and fears a government that won’t let you undersell your politically-powerful competitors. For Friedman, Pinochet is a bad–an aggressive, powerful military dictator–whose evil the Chicago Boys can curb by persuading him to adopt laissez-faire policies.
Roughly speaking, Friedman’s position was that even a dictatorship (such as Chile or China) would be better off with free-market economic policies. Hayek’s was to prefer a liberal dictator to a democratic government lacking liberalism.