Is it harder to lead a disobedient subordinate or an apathetic subordinate?

Apathetic. They've already given up. Disobedient means they have the will to fight. They are fighting AGAINST something. We just don't know what yet. Once you know what, you can adjust motivation techniques. With an apathetic troop, they are just riding it out, and your goal is keep the attitude from spreading to others.

I would say Apathetic. This person has already made up their mind they will not do anything you tell them. A disobedient you can talk to and work with them. Where as an apathetic person there is no reasoning with them.

Disobedient subordinates can be dealt with quickly, either correct your actions or start UCMJ or Chapter paperwork. Apathetic subordinates are a much harder animal to deal with, as they generally know the regulations and skirt right up close to the line without crossing it and so therefore require more effort from their leadership to adjust their actions. I believe that apathetic service members are far more detrimental to an organization than disobediant, because for the most part service members know right from wrong and therefore will police up the disobediance, but apathy can be contagious.