This paper examines the factors that govern persuasion for a priori UNDECIDED versus DECIDED audience members in the context of on-line debates. We separately study two types of influences: linguistic factors — features of the language of the debate itself; and audience factors — features of an audience member encoding demographic information, prior beliefs, and debate platform behavior. In a study of users of a popular debate platform, we find first that different combinations of linguistic features are critical for predicting persuasion outcomes for UNDECIDED versus DECIDED members of the audience. We additionally find that audience factors have more influence on predicting the side (PRO/CON) that persuaded UNDECIDED users than for DECIDED users that flip their stance to the opposing side. Our results emphasize the importance of considering the undecided and decided audiences separately when studying linguistic factors of persuasion.