Jo Nova points to the excellent Keynes versus Hayek rap videos and compares with global warming views. My own observations are more to do with the nature of theory.

To compare Keynes & Hayek, I believe that we need to separate Keynes from the mainstream Keynesians. Keynes saw theory as a means to get the policy he wanted. It was the Keynesians (starting with John Hicks’ IS-LM analysis) that started the modelling approach. Both Keynes and Hayek eschewed the mathematical modelling of modern economics. In this Keynes would be closer to the perspective of GLS Shackle than Keynesians

1. Keynes saw the economic system as being essentially unstable. There was no tendency for the economic system to tend towards an optimal equilibrium. Rather it could get stuck for long periods with high unemployment. This seems to parallel to the notion of tipping points. The Keynesian multiplier The parallel in CAGW theory can be seen in the positive feedbacks and tipping points. When Bob Carter says that climate is homeostatic (or Warren Meyer at climate-skeptic uses his ball in a bowl illustration), they criticize the climate models for being Keynesian. I would think that the Carter/Meyer view of climate is similar to that of Hayek on economic phenomena. Climate is essentially chaotic, having only general empirical regularities. However, it has tendencies towards equilibrium. Please note that Hayek occupies a position close to Keynes this issue. Walrasian General Equilibrium with perfect knowledge and instantaneous leaps from one equilibrium to another is an extreme caricature of more mainstream economics. Here Keynes v. Hayek is more apt for the views on climate.
2. Keynesians view all the essential features of the economic system as being essentially knowable, capable of being reasonably represented in mathematical models. Hayek calls this a “pretence of knowledge” (the title of his Nobel Prize lecture), as although we may know essential features of the system, the relationships are highly complex and changing. The problem is not just lack of measurement, it is having data that is capable of being modelled in order make manipulation of these variables possible. In economics, the manipulation is control of macro economy. In climate, it is to control the global average temperature.
3. Keynesians believe that a few major measures are sufficient to describe an economy. CAGW theorists believe that the global surface temperature and atmospheric CO2 are key measures. Hayek questioned whether such variables were meaningful. CAGW theorists are on much shakier ground than the Keynesians here. Bob Carter points out in his book that the stored heat in the atmosphere is a tiny fraction of that stored in the oceans. When it comes to stored CO2 the problems are even greater.

But when it comes to the rhetoric of global warming, the analogy should not be with Keynes, but with Karl Marx. Climate models give true scientists perfect insight into the real nature of climate. Those who are on the outside are delusional and/or are either knowingly, or subconsciously, acting as lackeys of the oppressive class. In Marx the oppressive class are the bourgeois, in climate alarmism they are Big Oil.