In this study, we explore the impact of genre and navigation on user comprehension, preferences, and behaviors when experiencing data-driven disease stories. Our between-subject study (n=85) evaluated these aspects in-the-wild, with results pointing towards some general design considerations to keep in mind when authoring data-driven disease stories. Combining storytelling with interactive new media techniques, narrative medical visualization is a promising approach to communicating topics in medicine to a general audience in an accessible manner. For patients, visual storytelling may help them to better understand medical procedures and treatment options for more informed decision-making, boost their confidence and alleviate anxiety, and promote stronger personal health advocacy. Narrative medical visualization provides the building blocks for producing data-driven disease stories, which may be presented in several visual styles. These different styles correspond to different narrative genres, e.g., a Slideshow. Narrative genres can employ different navigational approaches. For instance, a Slideshow may rely on click interactions to advance through a story, while Scrollytelling typically uses vertical scrolling for navigation. While a common goal of a narrative medical visualization is to encourage a particular behavior, e.g., quitting smoking, it is unclear to what extent the choice of genre influences subsequent user behavior. Our study opens a new research direction into choice of narrative genre on user preferences and behavior in data-driven disease stories.