I found this great summary explaining how Hayek’s economics differs so much from Keynes’:
Hayek’s approach attacks, root-and-branch, the macroeconomic way of thinking. It is not simply a challenge to a particular theory of the determinants of mass unemployment, inflation, business cycles and the like. Hayek is not accepting the rules of the game or the parameters of the sub-discipline of modern macroeconomics.
Modern macroeconomics tends to assume that rules that apply at the micro level no longer apply (eg the Paradox of Thrift). Murray Rothbard in his History of Economic Thought (Vol 2, p195) had this to say on the split between micro and macro, beginning with David Ricardo in the early 19th century:
And here began the fateful and all-pervasive modern fallacy of a severe split between two hermetically sealed worlds: the ‘micro’ and the ‘macro’, each with its own determinants and laws.