Hayek had the intellectual firepower to take on Keynes. He was often exasperated by the inconsistencies in Keynes' work and his tendency to change his mind - something the Cambridge economist did quite regularly, and not only "when the facts changed".
But Hayek did not have Keynes' charisma and famous powers of persuasion. (The Austrian accent didn't help.)
Also, Keynes was telling politicians that intervention by policymakers could make things better, whereas Hayek was saying they would only make things worse. In the end, that made all the difference.
Hayek wrote a best-selling polemic railing against economic planning, The Road to Serfdom, shortly after World War II.
In it, he warned that the dead hand of the bureaucrat could threaten a free society almost as much as the iron boot of Stalin. (If he had written it today, I suspect modern health and safety regulations would have featured.)
After that, Hayek had years in the intellectual wilderness, while the Keynesians bestrode the world. But there was a last great burst of fame and influence in the 1970s, when he was awarded a Nobel Prize for economics and feted by free-market politicians on both sides of the Atlantic.
Lord Patten reports in the programme how Margaret Thatcher would pull favourite Hayek quotations from her handbag at key moments during cabinet meetings.