In general, does the state operate more or less efficiently than the market? More specifically...

What is the most efficient state run operation? What is the least efficient state run operation?

What is the most efficient market driven operation? What is the least efficient market driven operation?

My sense is that in general a market driven operation will be run more efficiently and practically than a state run operation. There may be particular instances of efficient state run operations that exist in the United States but there are always particular instances of efficient market driven operations too. Taken as a whole, we should skew towards market driven solutions.

I don't think that framing of the issue is very useful on its own. Public and private entities both participate in the market, and the question of which entities are most efficient depends on which definition of efficiency one deems most relevant (i.e. which inputs and outputs one chooses to measure, and by which methods).

Also, people often attribute exclusively to government a class of dysfunctions or inefficiencies that have virtually nothing to do with an organization's ownership structure, but have a great deal to do with management structures typical of large organizations (e.g. wasteful spending due to "use it or lose it" budgets). With respect to these problems, I would be very surprised if substituting public vs. private does anything other than change minor details of how they manifest.

"market" does not mean "private". "market" means "competitive, instead of monopoly". They are orthogonal. You can have competing governments, and you can have private monopolies.

Utilities are natural monopolies. Not exactly the best fit for a market solution, especially when, as in this case, they are negative externalities borne by the public that the company is trying to avoid paying for.

The company will pay for nothing. Its a powerco not a mint. Their only significant revenue stream is electric bills (pole rental for telco fiber optics, pole rental for cable TV cables, all small amounts of money)

What we have here is a decision between one group of accountants getting electricity users to pay, vs a different group of accountants getting taxpayers to pay. The fraction of the population that are net positive taxpayers is much smaller than the fraction of the population that uses electricity, so in a democracy it would be surprising NOT to see the people deciding the few people who are net positive taxpayers will get the bill. The large chunk of the population that pay electric bills while being net negative taxpayers are not going to volunteer to pay more.

A counterpoint might be that binding private enterprise by strict liability rules might coerce it to be extra cautious not to cut corners that lead to fires -- as opposed to a state owned company which might have less to fear from lax practices.

Although, it's debatable how avoidable starting fires is in the bone-dry tinderbox of 21st-century California, even if you stick closely to best practices.

What you describe is exactly what PG&E is today. Those strict liability rules did not prevent them from cutting corners. They estimate damages at 15B and their insurance and assets are worth $5B. So do the math.... taxpayers will have to pay for rebuilding and if PG&E survives will they pass costs on to rate payers (aka the same people whose houses burnt down) or will they tax PG&E more or ?. Maybe PG&E will become insurance company owned since they will owe the insurers tons of money since they can't pay out for liability.

You mean the monopoly utility in Northern California called PG&E?