The outsourcing of public services is justified, when a government is unable to provide those services at a reasonable and sustainable level. For example, a rural area may not have the resources for public transit, or may not have the ability to provide it at a reasonable level. However, if a nearby city has the ability to provide this service, it may be done at a far lower cost and superior quality, than the rural area could provide. This could be extended to all public services, including utilities and aid programs. Consider developing countries without the ability to provide clean water, or sufficient electricity.
Outsourcing is not justified because it is not a cheaper solution. The government can pay the same price for employees and goods. This gives the government a competed advantage because they do not have to generate a profit. Based on this outsourcing is always more expensive. Republicans just want to give money to their friends.