The problem with private companies without any overlook, is that they can change on a dime. Private companies fail on a regular basis; if it weren't so, most of the companies that ever opened would still be operating today. Public agencies last much longer. Don't belive me, just look at the post office.
Although bureaucracies of all types can develop inefficiencies, there are fewer feedback mechanisms to correct inefficiency within the public sector. An inefficient private business can only survive so long before a competitor exploits their inefficiencies to deliver a better product at lower cost. The desire to remain competitive motives private companies to remain as efficient as possible. Public agencies, on the other hand, have different incentives. They answer not to shareholders but to politicians, whose priorities sometimes conflict with agency objectives.
Public budgeting also encourages wastefulness, as not spending all of an allotted amount will mean less money allocated for an agency in future budgets. This means money will be spent regardless of whether it serves any purpose. Political accountability through voting is too indirect to significantly mitigate this problem.
No, I think that the private companies are more efficient that the public ones, because the private companies want to push their companies as far as they possibly can, and get as much of their product out as possible, so they can make a lot more money for the owners.
My experience says public agencies are way less efficient than private companies. Public agencies usually seem to have a room full of people but no one comes to help you as you stand at the counter. If this were a private company, everyone would be cross trained to do everyone else's job. They would not allow someone to be left unattended at a counter while there were other clerks doing nothing. Private companies would have their eye on maximizing the labor dollars they spent.
I do not believe public agencies are more efficient than private companies. Essentially I think the overall efficiency depends on the manager or managing director of the company, but overall I would say private companies are more likely to be efficient. Private companies have to turn a profit, so they have an extra layer that protects them from lack luster results.