What "sector" something is in has little to do with being efficient, it's more the size of the organization. I've worked in both public and private, and both small and large in both of those. All large organizations are inefficient.
Privatization is not effective for everything, just like publicization is not effective for everything. There are some things that the private sector just won't be good at providing - and some things they shouldn't be making a profit off of.