There have been some interesting posts, particularly Bryan Caplan's on intellectual Turing tests, but I think there are a few fundamental misunderstandings of Krugman's claim that liberals know the opposition better.
1. There is no such thing as a "libertarian theory of economics". Libertarianism, like liberalism or conservatism, is a political position - an ideology even. It's not an economic theory. People are making a fuss over the fact that Krugman isn't making distinctions between conservatism and libertarianism and infering that he doesn't even know what libertarianism is. This is an absurd claim - of course he knows what libertarianism is - but it's also irrelevant. That's all politics. He is contrasting liberals with conservatives but he specifically mentions being able to describe the views of "saltwater economists", "a Keynesian economic argument", etc. etc. And of course, he specifically has in mind mainstream Keynesian vs. mainstream non-Keynesian (the so called "saltwater" vs. "freshwater"). In that face-off I think Krugman may actually have a point. Exhibit A is Casey Mulligan, Exhibit B is John Taylor. Smart guys by all means, but they have been a little disappointing through the crisis. A good example of what Krugman is getting at is when Krugman has to walk Taylor through his own Taylor Rule and explain why some economists have a slightly different view of what makes sense for the Taylor Rule even if it's not the "original Taylor Rule".
2. And then there are the Austrians. I just don't think he has them in mind here. It's simply not a rival school in any meaningful sense. I think it's interesting and I think it's worth talking to you guys, but not everything Krugman posts is a challenge to you. I think he mostly has other people in mind. So what about the Austrians? Krugman has definitely botched the theory in the past, and most other Keynesians couldn't explain it either. But when you look at guys like Don Boudreaux, Russ Roberts, John Papola, and even better Austrians than them it's pretty clear they do no better. They are probably more broadly familiar with Keynesianism than vice versa. I would agree with that. But there's still considerable ignorance on both sides. I think this has a different origin on each side. Most Keynesians generally ignore the Austrian school, which is the source of their ignorance. Most Austrians actually hold a distorted understanding of Keynesianism, and many (not all) attribute very bizarre ideas to Keynesians (like that they think the government can plan the economy, etc.). So this is a mess all around IMO, but ultimately I think not even what Krugman had in mind.
3. Caplan's Turing test idea is interesting. I think I'd do decently well posing as someone else. I think calling out someone who is posing is much more difficult. After all, there are really bad Austrian expositors of Austrianism and really bad Keynesian expositors of Keynesianism out there. A great idea, nevertheless.
4. As I said in the comments of David Henderson's post, I think it's inevitable that each side is overconfident, and there are a few good reasons to expect that.
5. This is also one of those questions where not only is it hard to find an answer to, but there might not be an answer to the question. Who belongs on either side, for one thing? And the distribution of knowledge is going to look really weird it's not like you're going to have two clean normal distributions with a clear winner, on average. You're going to have people like Bruce Caldwell and Barkley Rosser perform great, and you're going to have a huge group of people that do poorly. Ultimately this sort of test will be driven by the shape of the tails of the distribution, not by any center of gravity of knowledge. So what does that really tell us.
6. There's also a lot of disagreement! I don't agree with all the post-Keynesians. Are they "with me"? I would rule out a lot of Austrian explanations of Keynesianism as being absurd, but clearly they hold those views for a reason and they're going to challenge that. This is sort of where the Turing test comes in, of course, but even within a school of thought there are differences. If I talk like a Rothbardian, what will a Hayekian think? If someone talks like a Hicksian what will a New Keynesian think?
7. Finally, I think monetary disequilibrium theorists on both sides of the aisle will do comparatively well at Bryan's test.