No, its not simple. Event ABT proved the analysis was not simple and supposedly, their think tank is one of the best. Never, will anyone be able to compare to the penny that one is more efficient than the other. Nor, will anyone convincingly prove that one, in terms of quality of service is better than the other. Afterall, what do we want from prisons, public or private? There is no consensus on that.
I'm not 411, so I suggest you do a little research on those cost comparisons. The data is available. The hypothetical studies you can trash. Studies done by a so-called ex-professor you can trash. What comparitive studies are available support both sectors but do we suggest that if privatization saves a penny, it's more efficient.
Public policy is never focused on financial concerns. That's not what public policy is. We leave implementation of that policy to our politicians who seldom give a hoot what you and I think.