No, workers would benefit from private water more than public water, because a private company would be more careful. Also, private organizations would be more responsible to consumer issues and problems, because if they did not do a good job, the public would demand that their contract be given to someone else.
No, workers benefit more from private water, because private ownership gives a better incentive to take care of the water. If a person owns something, and it is valuable, they will take care of it. A person who owns the water will make sure that it is viable and that it will be profitable, and accessible to people wanting to buy it. Government rarely does things efficiently, so it is better for workers if water is in private hands.