Why can there be significant differences in public sector labor law across different jurisdictions?
Originally, your question made me stop a minute because there are so many different trajectories with which to take the labor idea behind your question. For example, the words "labor union" are very ugly words in the American South because it means, in essence, "worker's rights." In the American North, if a union goes on strike, and another worker steps up to the plate to take the unionized workers' place, they could truly get beaten and killed.
As a result, public Sector Labor Laws have been the topic of much controversy, especially in the last century. The question of whether to unionize or privatize is revisited over and over, with different areas of the country and different regions placing emphasis on worker's rights policies or emphasis on employer's rights policies.
The Northeast and Central areas of the country have seen much unionization and more emphasis on public sector labor laws than other areas. Strikes occur in various labor areas, and different regions are either receptive to these or discourage them with punitive measures.
There is also a dichotomy on what you might mean by the words "different jurisdictions." Certain groups of laborers are more likely to form unions and therefore have more effect on labor laws. Examples of these groups are Firefighters, teachers, and police officers. By joining together and pressing a collective issue, these groups are more likely to have more influence than individuals. Enotes gives quite a few good statistics on the subject:
All told, according to the Bureau of Labor Statistics, 14.4 million Americans belonged to a union in 2012. Nearly 36 percent of the public sector was organized; within the public sector, 41.7 percent of local government employees — most notably teachers, police officers, and fire fighters — belonged to a union.
Historically, unionization has been frowned upon in the South, and there were enough individuals in need of work to ensure that a strike did not have the same impact that it typically had in the highly unionized areas of the Northeast. Common strikes in these regions have led to more worker's rights and more humane working conditions.
The term "jurisdiction" in this context usually refers to the jurisdiction of each state. And it is the states that provide the law that regulates public sector employees, with the exception of those public sector employees who work for the federal government. Congress can regulate labor law for private entities under the Commerce Clause in the Constitution, but public sector labor law is a very different matter because we are talking about employees who work for a state, a county, or a municipality. So, it is the state that must regulate regarding these employees. The federal government cannot tell a state what to do or not do with its own employees. In recent years, various states have enacted legislation to take away various bargaining powers from public employee unions, while others have not done so, so far. Essentially, each state decides what to do about its own public sector employees, and the federal government cannot intervene to create some uniform scheme across the entire country. That is not an enumerated power under Article I of the Constitution.