Take the following with a "He's not an economist at all, and almost certainly has no idea what he's talking about! Get your head back in the clouds, cretin!"-sized grain of salt:
It appears to me that the Austrian research program works to establish a social scientific paradigm by which we can understand how individuals come to make choices, and to use that paradigm to understand why certain influences might be expected to have certain effects through their impacts on individuals' decisions. By defining terms in order to refer to very specific types of circumstances (to preserve the capacity for Misesian "a priori" reasoning), Austrians are vulnerable to an inherent inability to rigorously model social phenomena (insofar as they are acting as Austrian economists). But where Austrian methodology gives ground in its ability to model mathematically, it gains ground in its capacity to provide tools for understanding why social phenomena "make sense," or "might have been expected." That's why Austrian economics is often seen as being the only school that makes intuitive sense, and can be understood by lay people.
Where the Austrian program is a social scientific one, it appears to me that other prevalent schools of economic thought are more geared towards providing tools for policy making and forecasting. Through an Austrian lens, one might look at these schools as running a fool's errand; as statistical regularities are upset by fundamental changes in the nature of the phenomena with which they are concerned, economists' models will inevitably collapse with them. But as fragile as these models are, there remains a demand for them. And I think that Austrians are somewhat ill suited for creating them (though perhaps to their credit).
Today LvMI posted one of Hayek's lectures, "The Pretence of Knowledge," and in it there was a point I thought was extremely relevant here. In talking about mathematical approaches to economic modelling, Hayek said:
It has, of course, to be readily admitted that the kind of theory which I regard as the true explanation of unemployment is a theory of somewhat limited content because it allows us to make only very general predictions of the kind of events which we must expect in a given situation. But the effects on policy of the more ambitious constructions have not been very fortunate and I confess that I prefer true but imperfect knowledge, even if it leaves much indetermined and unpredictable, to a pretence of exact knowledge that is likely to be false. The credit which the apparent conformity with recognized scientific standards can gain for seemingly simple but false theories may, as the present instance shows, have grave consequences.
I think Hayek's point captures the sort of thing I'm trying to convey quite well.
To the extent that mathematical modeling and economic forecasting are helpful and useful, I think it makes sense to embrace the separate approaches to economics embodied in the current state of the profession. Austrian insights can help to inform the efforts of the more mathematically-minded economists, and remain valuable on their own. Of course, if the social scientific approach to economics is the only one that's worthwhile, then we would have reason to "advocate" Austrianism. But if there's a constructive role for both approaches, it makes sense to accept and preserve the distinction.