If privatization is done correctly, it can be a good thing. However, it can potentially be dangerous as well.
Private companies are, of course, looking to make as much profit as possible. This will mean that they will look for ways to cut costs when they run prisons. This could be a good thing if their cost-cutting is limited to areas where it is safe to cut costs. If this happens, they will still deliver vital services while saving the government money by cutting back on extras.
However, it could be that prison companies will cut costs in areas that are inappropriate. They might be less worried about providing a safe environment for prisoners. They might be less worried about doing anything to rehabilitate the prisoners. These are things that might be important but might also be ignored by a for-profit company.
Therefore, privatization could be good so long as the government makes very clear what services must be provided and at what level of quality. If that is done, private companies can probably save the taxpayers money.