If private sector is hired to uphold public sector's laws they should be able to do just as good of a job, hopefully lowering costs to the government while maximizing profit with more efficiency.

The only difference I can think of is the public's trust of government police, military, etc. I trust public or private military would not be bought off by the hightest bidder, committing treason. I trust that like a public municipal police force that a corporate municipal police force would be equally susceptible to bribes from private run jails to arrest more able-bodied men for their cheap labour.