In today's fast-changing world, it is essential not only to be innovative but also to innovate efficiently. The latter can be measured through the multi-faceted construct of innovation efficiency. While researchers recently have started investigating factors and practices fostering innovation efficiency, the fact that radical and incremental innovations require different structures and approaches has not been considered yet. This study, therefore, merges the innovation efficiency literature with the ambidexterity literature and divides innovation efficiency into exploitative and explorative innovation activities. As competition is an essential variable affecting innovation, this study explores its influence on explorative as well as exploitative innovation processes in terms of efficiency. Whereas exploitative and explorative innovation activities come together within general innovation efficiency to positively influence turnover growth, separately they have no effect on it. Data Envelopment Analysis is applied to determine the innovation efficiency, and ordinary linear and Tobit regressions are used to uncover different modes of operation of exploitative and explorative innovation activities. The results indicate that price competition hampers exploitative innovation efficiency, whereas explorative innovation efficiency might improve through outside pressure of product and quality competition. The results provide academics with a new perspective on explorative and exploitative innovation management, contribute to further detangling drivers and factors behind innovation efficiency, and help practitioners to better understand drivers of efficiency for the respective innovation processes.