I'm writing a fantasy and the main character has to either choose love or risk his life to defeat the bad guy. If he chooses love, he risks the world and gets his family. If he chooses to save the world, he risks his family and only may save the world. It's completely subjective and I guess the answer is whatever message I want to send is. But what I'm wondering is what do I call this? Is it love vs. duty? love vs. faith? Love vs. Morals? What's a good conflict for this?
As you said, it's entirely subjective and building a story around a premise (ie: love vs. duty) I personally find a very difficult way to write. On the subject though, think of white knights like Dylan Hunt from Andromeda who continuously spews and embodies the virtues of self-sacrifice and doing the right thing at all costs. Lots of bumps on that road.
Personally, I got sick to my stomach with love being the central theme in books and films. The sword of Truth series comes to mind as the worst one, where the MC can get both love and victory, and whatever else he wants. I know this is not what you asked, but I try to squeeze this wherever I can, hoping it would take: love is not important, nor is it interesting. Watching grass grow is more interesting. Seriously, if you wrote that a character was watching grass grow, I would break out laughing as opposed to him choosing between love and duty, which is the most common of platitudes in fantasy. Don't include love as a centerpiece in your work. Put it out there, i.e. he has a wife, or someone he likes, or someone he's currently with, but do not make the feelings they have for each other to be the most important theme, because, in all actuality, love may be the least important and the least interesting thing in the world.
As you say yourself, your feeling about this is personal. I like the stories I read to have love in them (though not as the one thing the entire story is centred around). For example, in the Emperor series Julius Caesar chooses duty over love, and in Imajica by Clive Barker (warning - spoiler) the main character chooses love above his own life. To me it's not the fact of a love-vs-something choice being present that makes a story good or bad, it is how the writer presents it. To the OP: It is your story and only you know what the MC has to do and why he will do it. Is it his duty as a knight, part of his religious beliefs, or simply because he does not want the world to end? Whatever conflict you choose, you have the power to make it fit. And, do you have to decide this now? Oftentimes, if you just continue writing the answer will eventually present itself.
Maybe you can leave that up to interpretation? Just write and let other people decide for themselves what he's fighting for.
Love vs. Justice? It was just the first thing I thought of. Not sure if it makes sense, but I figured I'd throw it out there.
The best classic concept I can imagine ... love vs honour. True love, whether it be with or against his family, vs honour and the responsibility to do what must be done. In a way, one of my current stories is about the love vs honor thing, but with a much different spin on it. More a love vs responsibility and in my works at least ... love always wins, the heart always tends to win over duty, responsibility, honor and everything else. You put your own spin on it, of course, but it all comes down to, what is the overall character going to do on either hand?
Love vs The Greater Good Or even something along the lines of sacrificing the world for yourself, or sacrificing yourself for the world
I'm with minstrel on this one: "Does it matter what you call it? Just write it!" I can't think of a reason why you would have to give it a label.