The aim of this paper is to shed light on the economic and epidemiological trade-offs that emerge when choosing between different vaccination strategies. For that purpose we employ a setting with three age groups that differ with respect to their fatality rates. The model also accounts for heterogeneity in the transmission rates between and within these age groups. We compare the results for two different contact patterns, in terms of the total number of deceased, the total number of infected, the peak infection rate and the economic gains from different vaccination strategies. We find that fatalities are minimized by first vaccinating the elderly, except when vaccination is slow and the general transmission rate is relatively low. In this case deaths are minimized by first vaccinating the group that is mainly responsible for spreading of the virus. With regard to the other outcome variables it is best to vaccinate the group that drives the pandemic first. A trade-off may therefore emerge between reducing fatalities on the one hand and lowering the number of infected as well as maximizing the economic gains from vaccinations on the other hand.