Interactive narrative is an approach to interactive entertainment or learning in which a system attempts to tell a story to an interactive participant. In this paper we report on a study to compare the theoretical strengths and weaknesses of two approaches to developing computational interactive narrative systems. We compare two approaches to interactive narrative: emergent approaches utilizing autonomous virtual character agents, and drama management approaches utilizing semi-autonomous virtual character agents. Our study uses improvisational theatre as an idealized, human analogue to computational interactive narrative. Results suggest that, regardless of approach, idealized interactive narrative systems should be nearly indistinguishable in terms of character believability and narrative coherence. Results suggest that drama management systems may have an advantage when particular features are required to emerge in players' interactive experiences.