The only benefit is not being hassled. If your foreign passport lists your place of birth as the country you are entering, it can cause a problem if you don't have the passport of that country ("Did you renounce your citizenship? What proof do you have that you currently are a citizen - we can choose not to admit you."). Also, entering your country of residence on a passport of another country (if you are a citizen of the country you are entering) can cause trouble ("How do I know that you are a legal resident your passport is from another country? I will hold you here until someone arrives with evidence." The threat was made but relented after some groveling.) I've had both occur. The remedy requires a lot of discussion (intense grilling in one case) and always has led to a warning. Carry both and present the one of the country you are entering. For a third party country it makes no difference except if there are different visa requirements.