Absolutely. My experience is completely anecdotal, and even if it's true that you get less bang for the buck in the public sector I still think it's ideologically sound and worth it. My country has a huge public sector but I think it's good.

What's normally the driving motivator in public companies to be efficient?

Professional pride?

I'd also add a sense of wanting to be useful, and not letting people (you serve) down (which can be emotionally draining).

My experience with the public sector is the same. People must spend all their budget or it will be cut next year, so they do. Processes calcify and no one is incentivised to improve them. It's hard to fire people or make them redundant, so people get shuffled around between departments, costing far more than they contribute. Pensions are often very expensive. Strike action is more likely, as it's a big mass of people who can shut things down.

Fundamentally, it's the principle-agent problem. The customer isn't the one paying the bills. The customer is a politician or two who can heap money on the department or not, and they get praised for heaping money rather than saving money. The people paying the bills, taxpaying individuals and businesses, must do so or they go to jail. So why be efficient when your customers cannot legally avoid buying your service?