The only time I've ever seen Germans say nein is in the movies or in textbooks. I've also heard a politician say nein when she wanted to make a strong stand again a comment. I'm guessing nein is more forceful and formal language than nee, which seems to be slang.
So I'm guessing if I don't want my language to seem weird I should use nee to negate a sentence and not nein, especially with younger people and in casual settings like a bar. Or is my impression wrong?