while the early Austrian School provided a lot of important insights, most of them have been accepted by the neoclassicals.
Neoclassicals are using some of the rhetoric of the Austrian School, but they are doing the opposite in almost every single issue: central banking, fractional-reserve banking, intellectual property, etc.
Those are three of very many issues: you failed to mention trade barriers, taxes, spending, government debt, regulations, price controls, rent controls, minimum wage, subsidies, and welfare.
All issues which Chicago School economists agree with Austrians, and which a surprising number of other neoclassicals agree too.
There is really no need to pick a fight between the Austrians and the Chicago School. Austrians are sympathetic to the Chicago School, particularly as they have adopted many Austrian insights. In fact, many of today's Austrians come from a monetarist background (Friedman as a gateway drug?), but later came to see how it is misguided and incongruous to oppose price controls on rent but support them on capital (interest rates).
The real conflict today is between free market supporters (Austrians and most monetarists) and the supporters of big government (Keynesians and the mercantilist-style neoclassicals). Unfortunately the latter have been commanding government policy for some time.
Neoclassicals are using some of the rhetoric of the Austrian School, but they are doing the opposite in almost every single issue: central banking, fractional-reserve banking, intellectual property, etc.