Mr. Omega said:
Going purely by story? Bioware. Capcom I think always delivers better gameplay, and while some of their business strategies are less than favorable, Bioware can be just as guilty in some regards. And while Bioware tends to do better stories, all their games are either medieval fantasy or sci-fi. At least Capcom has some variety in their stories.
I think Capcom's worlds are more interesting than Biowares. From Ace Attorney to Okami to Dead Rising to Megaman.
What I would like to see is if there's a game where Capcom makes the world and the gameplay, comes up with the level design, music, and characters, while Bioware takes care of the story, and character interactions.