Geoffrey Segal, writing for the Reason Foundation, did a 2008 article looking into the costs and benefits of the different ways of running a prison for a state government (although many of the points made are also applicable to local prisons as well). In his argument, he states that
"The Arizona Department of Corrections (ADC) recently released its latest cost comparison study between the ADC operated facilities and private facilities operated for the state. State law requires these occasional reviews to be conducted and the previous two studies found that the private facilities operated with significantly fewer tax dollars than their government-run counterparts, achieving cost savings of 17, 13.6 and 10.8 percent in 1997, 1998, and 1999 respectively. Despite this history and a clear track record of success throughout the country, the latest ADC review suggests a curious shift - that private prison costs were 8.5 and 13.5 percent higher than state costs."
Although this is an argument strongly oriented towards the ideals of the free market, it is still well-research and worth considering. Read the full article here.