Pros
Decent pace work. This can depend on your position. If you're a manager, expect to work a lot. Great work-life balance, plenty of PTO, benefits, easy mobility, & telework. This could be a great career for someone starting in the public sector without work experience. It can potentially open up plenty of doors for you. The department is fairly laidback & chill.
Cons
Low pay! This is probably the biggest one. You can get paid double or triple in the private sector. Your supervisor can make you or break you. If you have a bad manager, expect a horrible time working. You can be managed by a complete idiot. Everyone you work with is average. You might have coworkers with no college degree or just flew by college with an average degree or little work experience. Some of the managers have no idea what they're doing. It makes you think of the people who are qualified being managers.