Have they ever met, in any story in any medium?
Nancy Drew historian Jenn Fisher tells us that there were some Nancy Drew-Hardy Boys crossover books, but whether the two patriarchs met is to me a, um, mystery. (For some reason, only Carolyn Keene gets author credit on these. The two franchise also combined in six Choose Your Own Adventure®-style “Be a Detective” books, which were credited to both familiar psuedonyms, Carolyn Keene and Franklin W. Dixon.)