The post below cites some back-and-forth interplay on the variations between the Chicago school and the Austrian school (in the comments section), and I think a few people incorrectly focus on that main difference being anarcho-capitalism, which is not a fundamental concept of economic theory, and is not relevant to the Austrian school of thought.
First off, indeed, the fundamental difference between the Chicago and Austrian schools is methodology (inductive vs. deductive), and not anarcho-capitalism. However, as an aside, looking backward at the first Chicago school, under Frank Knight, it was fundamentally different even more so in that Knight eschewed empiricism and quantitative methodology, and he adopted an interesting range of theories, from the Austrians to the Marshellians to the Marxists. (Is there such thing as a Knightian?) When Friedman, Stigler, and Co. came along, positivism was used to prove out that goods were best produced under some form of “laissez faire” capitalism, which, of course, was not really laissez faire at all.Obviously, the two schools are radically different in regards to banking issues, and especially, public policy. The Chicagoans will devise every model possible to prove out how, where, and when intervention should happen in the economy. (See Bill Anderson on the Chicago school and antitrust.) The Chicagoans are also fully prepared to state how resources should be allocated based on those same empirical grounds. Yes, the Chicago school was once very unfashionable, and that was because they countered Keynesian tenets and the mistaken concept of “market failure,” and also, they were viewed as highly dogmatic.
I remember Mark Skousen once wrote a series of articles applauding the use of quantitative economics by some good, Austrian sympathetic economists, and he basically stated that the reason Chicago was so far ahead of the Austrians was because they positioned themselves on the inside (read: capitulated), and made the right players happy in Washington.
In regards to Ivan’s comment that the current Chicago school is not about free market economics, it’s important to remember perception, because, where the Chicago school is concerned, the pro-interventionist economists that he names (Becker, Stigler, Posner, Peltzman) are perceived as being representative of free market economics by mainstreamers. The current Chicago guys are who the media and think tanks turn to for a voice on “free market” issues, and that is because their answers are very much palatable to the masses and to policy makers.