I think this is one of those ideas that has been spouted for so long that we don't really stop to think about whether it is true. Private and public entities (and employees) certainly have different incentives, but they also have different mandates, and I've certainly known plenty of inefficient private enterprises and efficient public ones. Do you have any way of verifying or proving this idea that you can share?
A lot of people with considerable expertise in the area have looked into whether it's true. They almost always come to the same conclusion: overall it's a wash.
If you look closer some industries (like say your corner coffee shop in a big city) are clearly better off private, and others like roads and fire fighting don't work when privately held.
In general a competitive market will out-do public owned, free markets that aren't competitive are worse than public owned.
But there are always exceptions. A fine example is the health system. I don't know why, but as the US demonstrates even with a competitive health market public ownership outperforms a purely private system by a fairly large margin.