Having worked in IT with both the public and the private sector, my opinion is there is no difference in 'efficency' between them at all.

Efficiency seems inversely correlated with the size of the organization. Public sector usually has large orgs, but they are not run less efficient than equivalently sized enterprises.

You might jump to the conclusion that smaller entities would be the efficency solution, and even observe how this allows sometimes for a smaller entity to outcompete a big enterprise. However, if you approach it from a more systemic analytical point of view you have to take into account that surrounding the 'small' efficient business, there are dozens if not hundreds of unsuccessful competing small entities vying for the same niche. Taken together and purely looking at aggregate efficiency, this collection of competing businesses is even less efficient. The strenght of an openly darwinian struggle lies in innovation and adaptation, not in aggregate resource waste reduction.