A little bit of both. Magic in my world becomes stronger in a family the longer the line of Magi in it, since they tend to pass their knowledge and power on to the next generation. Since the Einzbern line stretches so far back, it makes them incredibly powerful, particularly in their specialties. So much so that they don't usually need to cooperate with other Magi, and since they don't need to, they usually don't. Most Magi are like that where I come from.