In recent years, the importance of mobile devices has increased for education in general and more specifically for science and mathematics education. In the classroom, approaches for teaching with mobile devices include using student-owned devices ("bring your own device"; BYOD approach) or using school-owned devices from central pools (POOL approach). While many studies point out features of mobile learning and BYOD that are conducive to learning, a research gap can be identified in the analysis of effects of mobile device access concepts on teaching-learning processes. Thus, this study aimed to empirically compare BYOD and POOL approaches in terms of learning performance and cognitive performance (subject knowledge development, cognitive load, concentration performance). Furthermore, the analyses included specific characteristics and preconditions (gender, socioeconomic status, fear of missing out, problematic smartphone use). A quasi-experimental study (two groups) was conducted in year 8 and 9 physics classes (N = 339 students) in which smartphones are used for different purposes. The present data show no group differences between the BYOD and the POOL approach in the group of learners with respect to subject knowledge development, cognitive load, and concentration performance. However, individual findings in subsamples indicate that the POOL approach may be beneficial for certain learners (e.g., learners with low fear of missing out or learners tending toward problematic smartphone use). For school practice, these results indicate that organizational, economic, and ecological aspects appear to be the main factors in deciding about the mobile device access concept.