There is an argument along the lines of "the risk of a project is the same irrespective of the method of procurement. But if the cost of finance is cheaper in the public sector, than it follows the overall project cost will be cheaper if procured by traditional methods". That argument ignores the reality of the procurement process.
Let us assume a Minister is about to approve commercial close for two hospitals for £100 million each; one to be financed by PFI, one by the public sector, using traditional procurement. At that point, the Minister will know that although the PFI's weighted cost of capital is higher, all the rigours of PFI procurement will have been applied as a precondition to obtaining the project's finance; the costs and risks will have been assessed and contractually mitigated at the outset. There is no such similar absolute assurance in the case of the traditionally procured project; its success will depend upon the quality of the procurement team in each instance.
The key point is that with two apparently identical projects, the PFI project is likely to be inherently less risky because of the imposed discipline of its debt and equity financers before the project commences. This benefit typically outweighs the higher cost of finances.