The government cost of borrowing is based on the assumption that governments have recourse to the taxpayer. In short, a government can increase taxes if it ever needs more money to repay its debt. In this way, there is no relationship between the risk of a project and its cost. As a result, traditional government financing can actually expose taxpayers to greater risk if investment decisions are made on this basis.
Under a PPP, on the other hand, financing is fundamentally different because the financing is non-recourse (that is, without the backing of the ability to raise taxes). All of the risk in a PPP is contained within the project. The only way the private partner gets paid is by building and operating the asset correctly, according to the project agreement. The cost to finance a project in this way reflects risk inherent in the project and, as a result, better project investment decisions can be made.
If the government were to issue project bonds directly, with similar non-recourse terms, the rate of return required by investors would be similar to the PPP cost of borrowing for the same project.