We should through this dichotomy out the window, along with vague polemic uses of the term "neoliberalism."
There's nothing vague about neoliberalism. It's a very specific, very definite set of political, economic and moral beliefs and assumptions with a very narrow base of advocates (although a plethora of useful idiots) and translating into very concrete policies.
That's a rather vague description for something so specific.
The term over the decades has meant social market ordoliberalism, been used as a broad category including both Austrian and Chicago schools - among others, a synonym for 'Third Way' Blairites and New Democrats , and now whatever this thing is that you are talking about. The term is more confusing than enlightening.
I'd argue that the Austrian/Chicago schools have almost no real life influence, so we're really talking about Blairism, which is the dominant ideology of Davos, Bilderberg, etc.