I think there's a big difference there, Friedmans advocate for some inflation. Austrians for pure sound money.
Discussion
That's not core to their arguments for these systems however. They wanted predictability and taking it out of the hands of arbitrary issuers, precisely because of the perverse incentives of the central bank, the lack of predictability or reliability, and the bias and misunderstanding of a board of governors unequipped with the information to dictate policy for the genuine benefit of the broad public.
The assumption of the necessity of inflation is merely a side concern subject to independent reevaluation in the positivist's view. This is information that would feed into the specific parameters of the algorithm of Milton's monetary policy machine or into the basket of commodities used for David's commodity-pegged network. It does not change the essential nature of those machines, of which Bitcoin is the full implementation.
When a Friedmanite identifies the broad effects of deflationary money, with its provision of retirement accounts for the average worker, its tendency to reduce overconsumption, the proclivity for the market to start to address externalities on its own, its freeing up resources for longer term thinking, cultural flourishing, more efficient investment, etc., the Friedmanite acquiesces, embracing hard money. I did. It is the only rational way, even for an economic positivist, in the face of both the logic and the evidence.
I disagree, the same way that any being with intelligence will prefer real hard money instead of inflationary money. Friedmans are utilitarians relativists.
I think these two outlooks converge if you are thinking deeply enough about it. What is higher in utility is achievable through better quality savings. Utilitarians who reject sound money are not consistent utilitarians. They're just doing it wrong and if they wanted to do it right and had occasion to go over the facts, they'd accept sound money. Else they keep deluding themselves. The Friedmans are mixed on that account but they far surpass most "economists" outside the Austrian school.
Murray Rothbard talked about how utilitarianism cannot get libertarianism right, but I think that is misguided: a proper understanding of utilitarianism in the broadest sense across a society (which is hard to achieve) is always equivalent to the natural law reading of things, because adherence to the natural law is what brings about prosperity in all cases when we define our rational actors with a sufficiently advanced understanding and long time horizon. Utilitarianism and positivism are thus extremely prone to error. It is an inefficient way of getting to the same answer that rational analysis provides, but it can yield interesting new details, particular states of affairs, and further hints for questions of rational inquiry, thus occasional empirical analysis is a welcome complement to the a priori rational method, in my view.