If the current poll results are any indication, it's not even a contest at this point. Gameplay is the main priority for a video game, fighting or otherwise.
That said, a good story can greatly increase immersion. Knowing who the characters are, their reasons for fighting, and seeing them progress in their individual quests creates attachment, and gives us something to talk about aside from combos and frame data (no offense intended). Honestly, if I didn't know anything about the characters, I don't know if I would've stuck with the series as long as I did.
Unfortunately, I don't think SC has been particularly good at storytelling. Only part of the cast has actual relevance in the overarching story, while others are just... there. The games rarely show the characters interacting, aside from specific endings and cutscenes (most of which aren't even canon). The bulk of the story is otherwise told via descriptions and narrative exposition, which breaks the pacing and shatters the illusion of being actually inside the world, watching events unfold (or, in the case of video games, actually playing a role in these events).
Although SCV's presentation is pretty lackluster, it's also the first game in the series that actually tried to tell a deeper story about the world and its characters. And I think it's a step in the right direction to actually do justice to the cast. I can only hope that Project Soul has learned from SCV and will give us an actual, immersive tale of souls and swords in the next game.
