Division seems to be focused on reponsibility. Basically "With great power comes great responsibility." The difference between skybreakers and dustbringers seems to be how they take responsibility. Dustbringers seem to do so via internal self-mastery whereas Skybringers do so via submission to an external set of laws. The dustbringer half is less certain since we haven't seen much of them, but the profile of the order from the radiant quiz mentions this idea of self-mastery.