I actually have experience with this issue! When I was on active duty in the Army, we had group of 4 Soldiers (3 senior NCOs and one officer) running a training program. When it was transferred to DA civilians it took 12 people to do the same job. When it was "contracted out," the team ballooned to 28 and extensive delays and failures occurred (like the loss of ammunition and weapons). The cost also more than tripled.
Rarely, if ever, do public-private partnerships benefit the public. Now, in some circumstances, governments can avoid capital costs for, as an example, purchase of expensive equipment (say, road graders), or for specialized expertise. For short-term, discrete projects, contracting can make sense. Similarly, bulk purchase contracts can save money. But I've seen more government waste in contracting than any other government process. To begin with, "profit" has to be added to almost every contract, even when it is not "earned".