Question: I'm a firefighter and would like to know when I should focus on losing body fat or concentrate on getting stronger.
Answer: This is very hard (impossible) to answer - which is why the fire dept. and others developed tests to measure your physical aptitude. It's more about "can you do your job well" rather than "can you look like you do your job."
The problem has become (painfully so) that the standards have dropped in physical tests. In doing so, just about anyone can "do your job" when in reality, they potentially can't do the job well. There is a huge difference.
I would ALWAYS err on the side of the "can you do your job well" mentality - and not just well, but you better be able to do your job and pick up the slack of the others who don't adhere to high standards. You may have to drop some body fat but I'd rather have that be as a consequence of improving performance. I'm also of the mentality that if you want to lower body fat, quit training/eating heroin-chic and start gaining muscle. I'd rather you gain muscle and thus improve your body comp - than lose body weight and muscle and simply weigh less.
I'm not asking you to become Joe Bodybuilder. I'm telling you that if you look at improving bodyfat % differently, everything might improve.
Also, I'd look at the dept. standards and then have your own Standards (obviously higher). One thing that I stress to the guys on the team is that part of being a man (or anyone in society but this specifically is about these young men) is that you MUST CARRY YOUR OWN WEIGHT/WATER/RIFLE. Don't be the guy that everyone has to pick up. Don't be the guy that can't run, can't fight through discomfort, can't be relied upon to be on time, can't do a damn push-up... who wants some teammate next to him who can't push his body up from the ground without sagging like a fried egg? Total lack of respect for everyone around you.
I'm not saying you don't carry your own weight but people in general need to up their pride. And no, I'm not talking about disabled people or the mentally ill. If every remotely able person carried his own weight, we could EASILY carry the ones that really need it.
In conclusion - higher expectations, don't get flabby.