As far as I know there are still quite a large number of private prisons in the US (correct me if you have some more up to date figures). So if this qualifies as a success I don't know...
I remember reading an article on private prisons in the US, about 3-4 years ago, although I can't remember where I read it. The article was very critical of the private prisons, because in order to be profitable they had to work with fewer guards and give the guards less training, so overall there was more violence and attempts to escape than in government run prisons, and more abuse of the inmates. The article also said that government run prisons had better facilities and programs for rehabilitating prisoners. I didn't treat the article too seriously at the time, as it seemed to me it was a bit biased. Now I'm not so sure