A private company is absolutely more efficient than a government. The boss simply says "this is what we're doing" and that's it -- it's just a question of what goal they're efficiently pursuing.
The problem is that intelligent, empathetic, and selfless people rarely rise to those positions. The few that do usually get pushed out of business by ruthless assholes.
I dont think that private corps with tens of thousands of employees can do that at all. Private companies also have committees and working groups and different departments that dont talk to each other (despite the committees), and policies that people follow even though the policy hasnt been good for years.
The boss says "this is what we're doing" and then it takes years for those hundreds of departments and tens of thousands of people to do it. Or they dont do it, because they disagree with the boss and the boss is far away from any work that they have no idea if people are doing it or not. Or they sorta do it, but then a new boss comes in and has a different plan.
Despite the dictatorship of the owner in a private corporation, actually implementing a thing, especially a new thing, does take a lot of time.
People forget that 'efficient' in a capitalist sense means that all resources are used. So when you privatize security, prisons, public transport, etc. guess what happens: those companies try to extract as much value as possible and do as little as possible. Because that is what capitalist efficiency is.