One big difference is management control. People feel that government administered services tend to have poor management and citizen services more often than not. One big example is the DMV since almost every has experience dealing with it, long queue times are almost universal because no one gives a crap and it's very hard to fire a government employee. Or the passport issuance, or applying for permits. Or unemployment benefits, the list goes on and on.
Imagine if the DMV and passport services had even the possibility of competition like a private company has. You bet all of a sudden the service would get much faster and better and with fewer mistakes and red tape with the same or fewer number of employees. Or someone would set up a competitor and imagine how many people would even pay extra just to not waste several hours of their time.
It's tax payer money so there is a lot more waste than even at big private companies. For example, the costs to just administer and operate the social security administration(not including any money paid out to recipients) is $15 billion dollars with a big B. There is no incentive for anyone to save the tax payer any money and there would be a huge pushback from govt contractors, unions and employeees. See how much hate DOGE gets for even proposing cuts or higher efficiencies.
Any large IT project in the government in almost any country and at any goverment costs huge amounts while not returning much value if any. Look at the state and costs of local metro stations and trains in almost any city.