My experience tells me that private industry is more efficient as profits, etc. are on the line.
========================
Your brain ought to tell you that the private industry will fail if it does not turn a nice profit, at least 15% annuallly and needs to grow or perish, while a government provides its services at cost, and has no need to grow at all.
If a government enterprise is i9nefficient, it is most often because some politicians decide to stuff some pork in the mix.
Agfa film was run by the government for over 30 years by the government and sold film for less than Kodak.
The Alaska railroad was run at a profit as a government corporation for years, until statehood gave Alaska politicians to screw it up.
Compare UPS service and cost with the USPS, and USPS wins hands down: better and more convenient service at a lower cost and with higher wages for its workers.