Not really, there are examples of private systems that are much cheaper than a lot of the state owned peers.
Also, if the government system is cheap because it is being subsidised it's not really cheap.
Governments have a way of under charging consumers for years, while letting assets depreciate, then when they need to be replaced, they are counted as new investments and funded by new debt, and then those assets get depreciated while consumers are under charged, never actually retuning any "profit" to reduce the loans incurred, thats subsidy.
Telstra is a good example, over the 20years or so since its been private costs have fallen. Today you pay less than you probably did 20 years ago, and get more.
Is that due to privatisation, or due to the ACCC allowing access to Telstra's infrastructure, which the public paid for.
The overseas companies didn't have the cost of the capital outlay, they just had to install equipment in Telstra exchanges, then they could offer the service at a much reduced price.
To say privatising Telstra drove down prices, is a bit of a con.
In a way the public is being taxed twice, for the infrastructure, they have paid for.
The public paid for Telstras infrastructure, but were receiving a dividend, due to Telstras profits.
The Government sold of Telstra, and allowed overseas telecom companies cheap access, to the existing infrastructure.
Now the public is being taxed again, to replace the privatised infrastructure, so the private companies have a better product to sell back to the public.
So with the NBN, the public are replacing the system they paid for originally, so that the private telco companies don't have to pay for it, sounds like a great scam to me.
It is just another case of "rope the dope".