The objectionable thing about the "grab them by the pussy" tape is NOT that Trump dared to use the word "pussy" in a private conversation that ended up being recorded.
The objectionable thing is that it indicates that Trump has, on multiple occasions, grabbed women's genitalia without their consent, purely because he's a celebrity and nobody stops him.
If Hillary had said that she had gotten Col. Ghaddafi "by the balls", I agree that nobody would have batted an eyelid because everybody would have understood that she was not discussing a situation in which she habitually sexually assaulted men and was able to get away with it because she was the Secretary of State.