Working for the government is not like working for a private sector company. There are some who would like to see that change, and perhaps over time some of the conditions that currently separate the two fields may be adjusted. For now, however, the distinctions exist.
Those with solid experience in employment law would likely agree that the one factor that divides government work from most other jobs is that employees enjoy particular rights of due process. These have their roots in the U.S. Constitution and Congress decided to apply them as a way to reduce political influences and promote more efficient conduct of government business.
Another factor that deserves to be acknowledged as a differentiator is that, in addition to the due process offered under civil service laws, many federal employees are also represented by unions. This means that if and when employment disputes arise, workers have a choice of whether to pursue action through a union grievance or through the civil service appeals process.
Which should be used depends on the specifics of your case and consulting with an attorney you have confidence in is the best way to make the determination.
There are a couple of things that tend to recommend the civil service route as the preferred option. For one thing, it calls for a precise set of procedural steps. Clear notifications of intent are required. To instigate an action, the employing agency has to provide evidence and share it. Levels of appeal also tend to be greater.
And, of course, while state and federal laws may be similar, they can differ. That being the case, to be sure your due process rights are fully exercised, it's a good idea to have the benefit of skilled counsel.