The response should emphasize the advantages and benefits of their particular training program. It should also clearly articulate what they DO NOT offer. For instance, I do not teach youth, physically disabled, or elderly students. Such an approach helps a student make a cross comparison between organizations and identify that which best meets their individual needs. Be wary if they make disparaging remarks about competitors or excessively beat their chest.
War stories are appropriate in a teaching setting if they illustrate a point or add humor.
War stories for the purpose of ego inflation is a cautionary indicator. Shooting instructors, for the most part, have enormous egos. It is necessary to the accomplishment of the mission, but the egos need to be managed. There are serious divisions within the shooting community among disciplines, schools, and instructors over methodology, standards, techniques, and simple personality clashes. However, instructors should observe professionalism when discussing other instructors or institutions.