As someone who has also worked in both the public and private sectors, I’d also like to add that there are fewer opportunities for real advancement in the public sector because of the fairly rigid hierarchical structure, tenure, etc.
You also have to deal with a lot more BS in the public sector because it’s more difficult to transfer to another employer, largely because you don’t want to forfeit the benefits and tenure earned with your current employer. It’s “job security” when you like what you do, but it’s “being stuck in your job” when you don’t.