Forecasting the spatiotemporal spread of infectious diseases during an outbreak is an important component of epidemic response. However, it remains challenging both methodologically and with respect to data requirements, as disease spread is influenced by numerous factors, including the pathogen's underlying transmission parameters and epidemiological dynamics, social networks and population connectivity, and environmental conditions. Here, using data from Sierra Leone, we analyze the spatiotemporal dynamics of recent cholera and Ebola outbreaks and compare and contrast the spread of these two pathogens in the same population. We develop a simulation model of the spatial spread of an epidemic in order to examine the impact of a pathogen's incubation period on the dynamics of spread and the predictability of outbreaks. We find that differences in the incubation period alone can determine the limits of predictability for diseases with different natural history, both empirically and in our simulations. Our results show that diseases with longer incubation periods, such as Ebola, where infected individuals can travel farther before becoming infectious, result in more long-distance sparking events and less predictable disease trajectories, as compared to the more predictable wave-like spread of diseases with shorter incubation periods, such as cholera.