Another game I really, really want to revisit. I remember my experience with FF XIII was that yeah, it was definitely the most linear out of all the games in the series, and the character progression system was a lot of bling, but not much substance underneath, but I also remember loving the music, loving the characters, loving their interactions, loving the battle system.
I don't really remember where these two songs play, I agree that Fang's Theme doesn't really give much of a hint to the character, though you're definitely right with your "warrior" feeling, I can tell you that much. Even within the same game, there are character themes that would better fit the bill of what you were expecting, like Sazh's Theme, for example. Fang does have a badass design, however, easily my favorite among the cast.
As a sidenote, it's really amusing, watching you react to FF XIII music, seeing you appreciate the art while mulling over all the polarising things people say about the game itself. I would recommend it, personally. From what little I know about you from watching you these past few years, I think you'd have a good time.
Cheers!