Before giving my take on this, we should never-ever-ever forget that, no matter what differences there are in the ‘Austrian’ school, that ‘we’ are more connected to one another, then we are to the mainstream ‘in general’. Adding to that: we should also remember that the mainstream is becoming more and more ‘Austrian’ - no matter how you define it. Compare Samuelson’s ‘Economics’ to Man, Economy & State: you’ll see 2 different worlds; as if they weren’t talking about the same thing.
If you, however, compare Mankiw’s economics too MES or other stuff published by Austrian’s now a days: you’ll see more and more overlap. We mustn’t forget that ‘most’ economics - especially the ones who make valuable contributions - in the mainstream acknowledge that the market isn’t a static, perfect competition thing in real life. That doesn’t mean they will acknowledge praxeology, entrepreneurship as fundamentally uncertainty bearing or whatever. It does mean that they will acknowledge more arguments that Austrian stress then 50 years ago.
I’ve got to admit; I’m more of a big tent Austrian, by which I mean a lot of economics can be reconciled with Austrian insights, e.g. modern New Institutional Economics, Public Choice, etc. The reason why I call myself an Austrian, is because the quintessential way I see the methodology of studying the market - and the market itself - through Austrian glasses: cause and effect, realism, change, useage of ERE, verstehen in stead of erklären, etc.
On the differences between Shackle, Lachmann and Hayek with ‘standard’ Rothbardian thought, the paper to read is Selgin’s ‘Praxeology & Understanding’. You can find the link here.
Basically it pertains to the uncertainty of the future, i.e. lachmann thinks of the world being ‘Kaleidic’ with radical uncertainty, while the standard Misesian vision is that there is such a thing as uncertainty, but it amounts to caseprobability, i.e. you can make reasonable and less reasonable statements about it and act upon it. There is uncertainty that you might not leave your house today, but nonetheless you can make a reasonable guess what will the most likely outcome to the question wether or not you’ll leave your house today.
I would argue that a lot of the ‘differences’ between the 2 main lines - one associated with GMU and one with the Mises Institute - isn’t as a big as some would like to argue. (Obviously; I’m not talking about strategy, personal differences, etc. I’m talking about the way they do and see economics.) E.g. Klein’s new book on enterpreneurship is very interesting and gives a different focus then Kirzner’s ‘Competition and Entrepreneurship’, but I would argue that the difference is smaller then some (including Klein, I think) would argue. The whole discussion on ‘full’ or ‘fractional’ reserve banking is completely irrelevant, in the sense that the economics behind is, for the most part, identical. ‘Monetary equilibriumtheory’ isn’t that much different as the analysis behind full reserve banking. The usage of equilibrium - between Hayek and Mises - isn’t that much different; the only thing that Hayek wanted to add is that economics should also take into account the way people learn in rl - whilst, if you stick to a pure a priori reasoning, you can just accept the fact the people learn and make mistakes. There is nothing wrong with that, but you can expand the body of knowledge if you think about those mechanisms too. Another example is the concept of appraisement: Salerno stresses this point - and deservingly so - but that doesn’t mean that the Hayekian point of being confronted with prices isn’t true also. (Only in a world were people appraise situations perfectly, there wouldn’t be a need for the Hayekian point.) Etc.
Summing up: it’s not bad to know the differences, but far more important than knowing the differences, is knowing the similarities and the way the mainstream is becoming infected with issues the Austrians have taken into account for years now. So we will be able to make valuable contributions. Yes, yes, they still take regressions. But the new and excited stuff in the ‘mainstream’ isn’t the next regression; it’s theoretical insights, who are more or less based on the recognition of causal mechanisms.