Brian Doherty has a good review of Wapshott's book here. The consensus (which Doherty agrees with) seems to be that Wapshott provides an unsatisfying coverage of the Keynes-Hayek debate. Doherty further suggests that Wapshott oversimplifies and even glosses over the economics debate itself. Unfortunately, I think Doherty is guilty of the same thing. Keynes - according to Doherty - believes that full employment should be pursued "by any means available", and Doherty is even more confused about the parameters of the disagreement when he writes "Keynesian ideas posited that free markets sometimes guided economies into ditches from which only concerted government action could pull them out". It's like the Cowen "this recovery makes Keynesianism a loser and RBC a winner" nonsense all over again! How many times do we have to inform people that this is not what we think until they finally stop insisting that we own up to it or defend it?
The most striking paragraph for me is this one: "For example, Keynes believed that intelligent, well-meaning planners manipulating economic aggregates such as demand and employment can bring about a happy end to business cycles. Hayek, by contrast, insisted that individual decisions and imbalances between specific prices and demand, or interest rates and specific plans for long-term productive projects, are where the economic action is."
"By contrast"? Now that's an interesting turn of phrase, isn't it? "By contrast" implies that what Hayek is said to have believed here is not something that Keynes believed. That's nonsense, of course. Those two statements are not opposites, Keynes believed both statements, and Hayek believed only one of them.