An excellent article in the New York Times from last week discusses how private prisons have failed to deliver on their promises of cost-savings in Arizona. In fact, "privately operated prisons can cost more to operate than state-run prisons — even though they often steer clear of the sickest, costliest inmates."
Private prisons essentially cherry-pick their prisoners. They take primarily low-level, nonviolent offenders, who cost less to house and maintain. They take mostly younger guys, and force the state to take older prisoners, who are more prone to costly health problems. They also rarely house high-security inmates.
In addition to all this, they cut corners on maintenance, have a horrible track record of denying medical care, and use significantly less staff than government-run institutions (staff costs being among the most expensive components of a prison's budget). They pay and train their staff less, and offer less benefits, which results in their staff being by and large less qualified and professional than you'd find in a government prisons.
Yet even after all of this, they still don't save a significant amount of money, and can even cost more to operate than a government-run facility. This study is just the latest of numerous reports that have all found essentially the same thing, going back nearly a decade. But our country's inability to enact effective sentencing and parole/probation reform to reduce our over-reliance on incarceration has caused governments to continue to perform this failed experiment with privatization. Hopefully, the decision that came down today in Plata v. Schwarzenneger will demonstrate that we cannot just continue to expand our prison population indefinitely.