how do labor relations practices in the public sector differ from
those in the private sector?

In the Private sector you are dead
- in the Public sector you are definitely dead within ten years

I worked in a union environment for over 30 years.  Federal law has a
lot to do with labor relations, but I had the impression that in the
public sector, there are more laws strictly controlling all aspects of
those relations.  Whereas, we were mostly only limited in certain
areas as a union.