and I’m wondering which faction is better for it. Neither seems to stand out in terms of Bleeding damage (although the Order apparently has some Vitality damage), and I don’t really know what else to prioritize.
I don’t really agree with that. Ring and Amulet augments are quite different between the two and should be considered. Kymons Chosen gives you access to the Kymons Fury augment which has +30% Bleeding (and +30% Physical, +2% DA).