COVID-19 contact tracing apps are one of the best tools we currently have available to avoid a potential second wave of COVID-19. However, sufficient critical mass in terms of uptake is required for these apps to be effective. Given the low adoption rate, a better understanding of the users' perspective is important to define measures to drive their adoption. Building on the privacy calculus, this study analyses the adoption of COVID-19 apps as a benefit-risk trade-off and provides empirical insights for Germany and Switzerland, which have been among the more successful adopters. Interestingly, we find many commonalities between both countries, which may be explained by their geographic and cultural proximity, but also with the similarities in app design and launch. However, we observe significant differences in benefit and risk perception between different groups of the population, which we classify as advocates, critics, and undecided. The findings reveal that all groups recognize the benefits of COVID-19 apps and confirm that reservations about privacy are the biggest hurdle to uptake. For the undecided and critics, our empirical data also confirms the privacy paradox, i.e. the differences between general attitudes and concrete behaviour.