Clearly, you can argue this either way. I will argue that the federal government should be in charge of running all the prisons.
The main reason for this would be fairness and equity. Under the current system, various states can have widely divergent prison systems. Some states can keep their prisoners in much harsher conditions than others, for example. This, it would seem, is unjust. A person's punishment should not depend on the jurisdiction in which he or she committed the crime -- the prison in which the sentence is served should have the same conditions, regardless of the state. For that reason, one can argue, a prison system run solely by the federal government would be superior to the system we know have.
I tend to think that some local control and decision making is likely a better thing than oversight or management at the federal level for all of the prisons in the United States. Of course, I'd rather have the federal government manage and run all the prisons than private corporations, but choosing the lesser of two evils isn't always my favorite.
Though it is difficult in today's world run almost entirely by legal minutiea, it would be helpful to have people running prisons who know the community in order to help make appropriate decisions regarding parole, etc., and having some familiarity with prisoners and police, etc., would also lead to better management of prisons.
The federal government cannot legally run all prisons. Though few of us know it, all US citizens hold an odd sort of dual citizenship. We are subject to both federal and state laws. Just to confuse thing further, a law or act may exist on the federal level but unless the police power is written into the federal law, it falls to the state to enforce the act. Social Security Disability is a case in point. Disability is a Title II benefit but the police power was not written into the federal act so each state processes the claims of its citizens.
Likewise, a shoplifter (outside of Wash DC) doesn't break any federal law so it's up to the state to deal with it.
Interstate crime, kidnapping, and so are federal crimes and any jail time is served in federal prisons, where there is no possibility of time off for good behavior. In theory, I would like there not to be 300 people on Texas' death row while there are none in Maryland. Having all prisons run by the federal government might eliminate some injustices in our system.
However, I don't feel compelled to rehearse the Federalist Papers yet again. So many states are nearly bankrupt and I can envision how easy it would be to for the federal to step in "to save the day" but end up simply further eroding states' rights. A tough call.