shall I tell the director the truth....--please help

I'm leaving the company in two weeks. The true reason why I jump the ship is my boss did not assign me the projects (higher visibility) or responsibilities as much as to the others who are in the same position as I am. I don't feel I'm much needed in this department. My boss' boss wanted to talk with me about my resignation. My boss and my boss's boss get along pretty well.I want to know if I should tell him the truth why I'm not happy and decide to leave. If I'm telling the truth, will that burn the bridge? Many many thanks.