Here's my logic train. Ultimately, in combat, sure, all bets are off. Kill the enemy, don't get killed. Accomplish the mission. All else, as the Baron said, is rubbish.
Outside that, our Sailors are a resource. We've got them for a fixed amount of time, and then they can decide to re-enlist or say "FTN, I'm done." Sure, some that leave are "addition by subtraction." A lot aren't. A lot are smart people we want to keep, and we as an institution should be doing our damnedest to be desirable to those types of people no matter what the economy. I'm not talking selling out. No one joined the Navy to be Jeff Bezos rich. But there is a moral and emotional itch that a lot of us scratched by signing up to be part of something greater than ourselves. To defend those who can't defend themselves. We didn't want to spend our 20s and 30s in a cube farm working for The Man.
But we get in, and our experiences are shaped by the leadership we have to serve under. Some people are transactional, and want to do their time, get out, use the GI Bill, and live their lives. Totally cool, and no shame in that. I mean it. But how many folks joined because they'd wanted to be an aviator (or a shoe, or a nuc, or an enlisted dude) since they were kids, get parked under some toxic asshole, and then we drive them out of the service?
When I read "many folks can't be both," I read an undercurrent of "do whatever it takes to get the job done. If in doubt, ride your people, because they can suck it up." I'm not saying
@Spekkio meant that, I'm saying that's what I read into it. Maybe I just ran across a couple asshole golden children too many on active duty, and it skews my perception (not that all golden children are assholes). I don't know. But when you ask "what is more important," there's an implied dichotomy of "you have to pick one or the other if you can't do both." And also an implication that "if you have to pick one, pick getting the mission done and be hated for it."
I'd submit a counterargument. Not every individual person is going to like you; that's just part of being human. But as a CO, DH, LCPO, or whatever, if you are not at least respected by the balance of your people, you failed. I don't care if you got the job done. I don't care if your ISIC gave you an EP. I don't care how many stars you put on. You're in over your head, you're a detriment to the service, and you should leave. I'd submit that "many can't do that" is false. Not everyone will be loved. We don't all have the charisma and savvy to do that. But the minimum for a Navy leader is to treat your people decently. Even if it means you don't get that next rank. People are not a means to an end unless missiles are flying. People are an end in and of themselves.
Your people (or most of them) will understand the difference between "good person stuck in a bad situation" and "asshole who just cares about looking good to his boss." There's "yeah, we were in some shit times, and CO/XO/DH/Divo/Chief made some tough calls, but he had our backs. Not the most personable guy, but he looked out for us." And there's "I'm getting out, because leadership doesn't care about me. I wanted to be an officer (or a Chief), but now that I've seen behind the curtain, screw that. Bunch of politicians." You'll get both from the same situation with different leaders.
Edit: A wise man once observed that you can gain the world, and still lose your soul . . .