A couple of things that might be mentioned about the private/public spending divide:

In many of the publicly-run institutions of the UK, at least in the UK, the people at the “sharp end” that actually do the work are actually grossly overworked and underpaid – also under-supported. This obviously applies to the military, but also to quite a lot of hospitals over here. It seems equally inevitable that any government-run organisation (and to be fair any sufficiently large private one, especially with a monopoly or close to it) accumulates a grossly excessive number of bureaucratic drones who do nothing useful whatever. THis part of it applies to the military as well; for example, at the moment the Royal Navy has more admirals (rear-admiral or above) than ships. I suspect that the USA is in a similar position.

Secondly, not all public spending is bad. Spending, for example, on new highways and bridges that are actually needed is spending on a public good, that no private organisation could realistically undertake. Spending on improved maintenance of infrastructure we already have is an even clearer example. One example of this in the UK is our water supply and sewer systems. I am told that one water leak near Manchester had been there so long that many people in the area thought that it was a natural spring. But there are no votes in water pipes and sewers, so…