Unions give employees more power to negotiate the terms of their employment, and that’s true of public-sector unions as well. However, public-sector unions differ from private-sector unions in at least two ways that may support treating them differently e.g. exempting them from some or all protections we otherwise provide to unions.
First, in a democracy, public-sector employees already have some direct influence over their employers, in the form of the democratic process of influencing policy through voting etc. In that sense, they function like co-owners. Private-sector unions typically don’t have this influence without unions.
This can have the effect of giving public-sector union employees multiple opportunities to effect their preferred policy outcomes: they can lobby, run candidates, and vote to influence the policies that will affect their jobs; and if they don’t like the outcome, they can organize a strike or otherwise leverage their union power to force those policies into place.
Second, private-sector unions serve as a check on the power of private ownership of companies, and limit the share of company profits that owners can capture. They serve to redistribute earnings between two groups of private actors.
Public-sector unions, by contrast, serve as a check on the government-as-employer. In a democracy, where the government works on behalf of the public, Public-sector unions serve to redistribute from the public coffers to private employees. So where they succeed, they do not necessarily have the same pro-social effect that private-sector unions have.
These differences undercut much of the rationale for union support, but may not eliminate it completely. Unions also allow groups to act in a coordinated way, and that may lead to better policies. For example, unions may help with price discovery: negotiating for wages individually will tend to under-estimate the value of the labor by favoring the lowest-paid workers, where collective bargaining may better identify the average value of the labor. That effect would apply equally to public-sector and private-sector unions.
So it may be useful to partially limit public-sector union activity rather than to eliminate them completely. That could mean protecting e.g. collective bargaining and union lobbying, while limiting the right to strike. Or it could mean prohibiting requiring union membership as a condition of public-sector (but not private-sector) employment.
Public-sector unions are relevantly different from private-sector unions. We should think about them differently, and we should probably treat them differently under the law.