Another interesting example, going back to the 1980s. At that point of course privatisation was the big thing - taking public owned businesses that were stagnant and unprofitable, and privatising them so that they would be revitalised and become profitable.
British Airways is a fascinating case study. If you remember, Sir John King was appointed to prepare the company for privatisation. He turned it around, from a serious loss maker, to one of the most profitable airlines in the world. Note, this was BEFORE it was privatised, while it was still publicly owned. It was then, of course, sold off.
The key lesson from that (and other examples) is that in practice it is not whether an organisation is public or private that is important, but how it is run.
Another unfortunate example, of course, is the contrast between the United States medical system (widely acknowledged to be vastly expensive for what it achieves), and the UK NHS, which has its failings but generally achieves a reasonable outcome with a relatively low cost.