Competitive bidding decreases the costs of operating the institution but the reduced cost has to show up somewhere in in the system either as poorer quality food, medical treatment or security. That may not necessarily be a bad thing when you consider the average cost per prisoner in a government institution is around a thousand dollars per week.
Between law enforcement and the penal system, one of the major costs to society is dealing with people that don't live by the rules. The privatilization issue depends on at what point the reduced cost becomes inhumane treatment.