From a purely selfish standpoint, I would love to see the source, as it is clear that the site has been done "correctly" in so many different ways, and I think it would make me a better developer.

If you did open-source it, you would have to license it in a way that protects you from direct competition, as I honestly think you guys should be the only ones in this space. Having two or more StackOverflows on the internet would only dilute the model.

I also think you should be very choosy about who gets write access to the code repository. These people would have to be totally dedicated to the purity of the Stack Overflow concept, and the only way to be sure of that is to retain complete control.

Undoubtedly you would face competitive pressures from clones who use your code. But your secret sauce is not the code itself, it's the social model you have constructed that is embodied by the code, and that has already been open-sourced.

I wish I had a crystal ball and could tell you what the best business model is. Nowadays its seems that the more you give away, the more exposure you get and (potentially) the more revenue you can capture. But I think you already have your audience. From a business standpoint, I don't see how open-sourcing StackOverflow will help you.