The difference is that public employment is open to the general public, and ALL workers benefit by having these jobs out there because, even if they don’t personally take these jobs, private employers have to compete with the public sector for good workers, and this puts a floor under wages and benefits for ALL workers — public and private.
Not only that, but when local workers are paid fair wages/benefits, the surrounding community benefits because it keeps debt-free money flowing through the economy. So, we get the double benefit of recieving high-quality services and keeping debt-free money circulating in the local economy. With private corporations, the wealth is funnelled to the top, and that money can go anywhere — different cities, states, or countries. The workers will be more likely to need public services and subsidies because they will NOT be paid living wages…profits for the corporation/executives are all that matter there.