Today, I was browsing through the FATE System Toolkit and discovered the section on scaling the stress tracks. Then it suddenly became clear what I need to do. Humans don't have stress tracks at all. If they are Supporting or Major NPCs, they take consequences right from the start. If they are mooks, they are taken out immediately. In FAE a mob of mooks would have a standard stress track. In FATE Core mooks would still get the supporting bonus. But if they take even a single point of stress, they are taken out.
Vampires on the other hand will have stress tracks, and probably complications acting as a blood supply, as suggested by one comment. Not sure how to go about this. The stress track of course represents the ability to shake of minor (and not so minor) damage. The complications will power the stunts and allow the vampires to get additional bonuses for physical feats.