Private owned vs. State owned” is the wrong debate. State owned monopolies do not perform well even if they perform moderately better.
Can this generally differ from country to country? I tend to agree with this in the sense that state owned monopoly tend to reach economics of scale as a result of large patronage, hence it's a no-brainer for whatever service they offer to be cheap. This doesn't mean because its cheaper than state owned that it might actually be better.
Nigeria is run and controled my private monopolists who are paying hugely to the government to be in that positions, what do I call this? Since its in between state and private?
However I believe private monopoly to be worse especially since there are no systems put in place to actually checkmate the excessive maniplulation of price to make more profit. Private monopolists are why entrepreneur are not given patents in the Nigerian market structure.
What you describe in Nigeria sounds like crony capitalism. The Government and the private monopolies are working together to get rich at the expense of the public. In western countries it is more difficult for them to get away with that. Therefore, we have oligopolies instead. They create the impression of competition but there is very little. In many ways they are just like monopolies.
Government monopolies can provide very low price services. They could even provide free services but that does not make them efficient or good. The taxpayers are paying for all of the Governments inefficiency and even corruption through higher taxes.
Nigeria is currently a developing country and to some extent, the principles of good governance is hardly applicable in so many aspects. In an economically adept country like you pointed out, this crotone capitalism might not work out, but this is to generally suggest to you that Nigeria doesn't have the structural framework that makes the economy to function as it should. Its totally saddening.