Austrians critique it on both fronts because while it claims to be inductive, it is often deductive – that is, they sneak in a proiri premises of their own while claiming to have none – and the Austrian critique isn’t just a tu quoque but that these premises are wrongheaded.
Note that almost all Austrian Economists with a PhD got theirs in “mainstream” economics, so they do know both arguments. Professor Herbner can certainly add more here but outside of LC, Robert “Bob” Murphy has given the best compare-and-contrast I’ve seen – he really breaks down the differences in a clear way. But this one by Walter Block is pretty decent too.
Edit: I also really like the two Israel Kirzner lectures that start with this one, which go into the whole background of the difference and the development, the intellectual history of the whole divergence.