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

Why don't you look at how you treat your subordinates.. I had a Staff Sgt who was from the upper east coast me being from Texas .. he thought I was a racist redneck and made my life miserable never gave me a chance to prove him wrong. I rotated from Germany and never saw him again. So why not take a step back and look at what the bigger picture is and evaluate the entire problem before saying the person is the problem. There are many jobs in the military some people are really good in some areas weak in others and sometimes the job they are assigned from MEPS isn't a good fit. Reclassification to a skill they are really good at may help and provide retention.

Depends on why they are apathetic. Perhaps it's not their response but the stimulus that's causing the issue

Both are bad news, and their attitudes can spread. I'd start documentation on both immediately. I'd also find out what the problem is if possible, and try to work with them to improve teir attitude and performance. Document that too. Start the discipline process as well. One thing that is going to be controversial, but often others in he unit will take matters into their own hands and give an attitude adjustment. As long as this doesn't go too far I say get out of their way, and even facilitate things if you can. But some people are just incorrigible. Get rid of them, and by that I mean out of the service.

Apathetic. They're weak minded.

Disobedient folks have a reason. Break the reasoning you got one of your strongest team members already

Apathy by far!