You're right, Keynes wasn't as far out of the mainstream of classical economics as many people think. But I think he did dismiss the importance of savings, which helped push 'Keynesian' economics into overweighting the demand-side and neglecting supply side issues. Personally, I rather like Schumpeter.
I think that Hayek would largely disagree even though he admired Keynes just not his theory, which I believe he thoroughly refutes.
Hayek DID foresee the Great Depression, he saw the same Govt interventionist activity in America as he had seen the Euro-socialists were up to before duped American Govt bought fully into it.
After all Hoover was actually the first New (raw) Dealer.
Hayeks biggest criticism of Keynes was Keynes statement that we would all die anyway eventually.
I suggest you do a little research on the matter at mises.org - a huge repository of Hayek & Rothbard articles there.
I'll take Rothbard and Hayek any day over all the others.