Talking bad

Is a jew allowed to talk bad about a noahide but a noahide not about a jew ?

Shalom U'vracha, Both of these scenarios are permitted. A Noahide is allowed to speak lashon hara about a Jew, since he is only commanded on 7 mitzvot, and lashon hara is not one of them. A Jewish person is also allowed to speak lashon hara about a non-Jew because the Torah says 'לא תלך רכיל בעמך'. This tells us that you can't speak lashon hara about your fellow Jew ('in your people') but you are permitted to speak lashon hara about someone who is not Jewish. However, it is surely not a proper thing for a Jew to speak badly about a non-Jew (or vice versa). Even though the Torah doesn't forbid it, it still is considered a negative deed. Sources and detail: Some say that although the Torah does not forbid a Jew to speak lashon hara about a non-Jew, there is an 'issur d'Rabanan, (a prohibition of the great Rabbis) because speaking lashon hara about a non-Jew may lead one to speak lashon hara about a Jew. (Rav Nissim Karelitz in chut shani, hilchot loshon hara 357, according to the midrash Devarim raba, ki tezei 6, HaravChaim Kanievsky also mentions as a possibility that there is an 'issur d'Rabanan). Others disagreed, (among them the Netziv of Volozhin (haamek sheeala 28;1) who hold that there is no d'Rabanan prohibition to speak lashon hara about a non-Jew. In practice, it seems that this is the simple halacha because if there was a prohibition it should have been mentioned in the Rambam, Shulchan Aruch, or other poskim. The Chafetz Chaim collected everything about lashon hara and didn't write that it is forbidden to speak loshon hara about a non-Jew. See too the Minchat Asher (the new version) Beraishit, (11:6) who brings different sources that besides the Seven Mitzvot of B'nai Noach, non-Jews are supposed to act kindly and to behave in a proper way. Therefore, S'dom was punished for not feeding the poor. Even though there is no exact commandment about it, G-d wants every person, non-Jews and Jews alike, to act with good character traits even beyond the exact letter of the law of that written in the Torah. Therefore both Jews and non-Jews should not speak badly about anyone even if it is no exact prohibition.