Despite the availability of vaccines, influenza remains a major public health challenge. A key reason is the virus capacity for immune escape: ongoing evolution allows the continual circulation of seasonal influenza, while novel influenza viruses invade the human population to cause a pandemic every few decades. Current vaccines have to be updated continually to keep up to date with this antigenic change, but emerging ‘universal’ vaccines—targeting more conserved components of the influenza virus—offer the potential to act across all influenza A strains and subtypes. Influenza vaccination programmes around the world are steadily increasing in their population coverage. In future, how might intensive, routine immunization with novel vaccines compare against similar mass programmes utilizing conventional vaccines? Specifically, how might novel and conventional vaccines compare, in terms of cumulative incidence and rates of antigenic evolution of seasonal influenza? What are their potential implications for the impact of pandemic emergence? Here we present a new mathematical model, capturing both transmission dynamics and antigenic evolution of influenza in a simple framework, to explore these questions. We find that, even when matched by per-dose efficacy, universal vaccines could dampen population-level transmission over several seasons to a greater extent than conventional vaccines. Moreover, by lowering opportunities for cross-protective immunity in the population, conventional vaccines could allow the increased spread of a novel pandemic strain. Conversely, universal vaccines could mitigate both seasonal and pandemic spread. However, where it is not possible to maintain annual, intensive vaccination coverage, the duration and breadth of immunity raised by universal vaccines are critical determinants of their performance relative to conventional vaccines. In future, conventional and novel vaccines are likely to play complementary roles in vaccination strategies against influenza: in this context, our results suggest important characteristics to monitor during the clinical development of emerging vaccine technologies.