Let's be a little more realistic about this: Austrian and Keynesian theories both exist to this day because they provide good enough rationalizations for the preconceived political agendas of different sets of people.

The idea that economics breaks down into a neat little disagreement between Keynes and Hayek, however, is anachronistic.

Austrian Economics uses praxeology, logically necessary insights in human action. Economics as a branch of logic.

All other schools (including Chicago) see economics as a branch of statistics.

This is a fundamental difference that almost nobody seems to realize.

Economics isn't a branch of logic (or, for that matter, statistics) any more than physics is a branch of mathematics. Rather, economists use logic, statistics, mathematics, observation, and in limited contexts experimentation as tools. It's a philosophical question of which tools to use that defines Austrian economics. Austrian economics is rationalist. Rationalism consists in choosing reasonable-sounding a priori assumptions and reasoning from them. Whether you're Descartes saying "I think, therefore I am" and deriving "God exists and is not an evil deceiver", or whether you're an Austrian economist saying "humans take conscious action toward chosen goals" and deriving "the gold standard is preferable to fiat currency", you're basically doing the same thing.

The ideal economic theory would be empirical, observing economic behavior and attempting to build models that fit to it. Both in philosophy and in the hard sciences, empiricism has won out over rationalism for reasons any decent philosopher or scientist could enumerate for you at length.

Behavioral economics is probably the best attempt at this ideal. You can view it either as a feature or as a bug that it doesn't tend to draw grand macroeconomic conclusions you can use to try and win political arguments.