BG said to be in favor of PPP for prisons in his post, because of government's scarce resources. He didnt touch on the most important issue, though. And, by the way, the lack of revenues argument is actually wrong since resources spent on prisons are resources non-spent elsewhere always, independently from the identity of the provider: at the end of the day, society has to somehow pay for the fucking prisons, Bruno. Or are you planning to provide them magically for free? The real issue is efficiency then, but in a broader sense, as I explain below.
Private or public provision?
Aside from the obvious case of near-pure public goods, economists generally are staunch advocates of private provision, even when financed via taxation (voucher for poor children to study in private schools, for instance). The reason is well known: the power of markets to deliver efficiency, align incentives, tame principal-agent problems within firms, etc. Competition is the name of the game behind the first-welfare theorem and high-powered incentives are a good thing, absent externalities. But does this last assertion always hold?
In a prison, the final service delivered is not easily verifiable, and the "client" directly involved does not really has a say in the process. Private competition and high-powered incentives are thus suboptimal in this setting. Private prisons will likely compete among themselves to the detriment of their direct client (the criminal), not to his benefit: cutting on food quality, accomodation standards, etc. And the client cannot -- literally -- vote with his feet in this case. Finally, in this case society and even public inspectors will have a hard time verifying and enforcing quality standards.
That's why when it comes to prisons even hard-line neoclassical economists tend to prefer public provision, or at least (but this is hard to implement) well-crafted soft incentives.