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In this work, we show that it is possible to train low-level control policies with reinforcement learning entirely in simulation and, then, deploy them on a quadrotor robot without using real-world data to fine-tune. To render zero-shot policy transfers feasible, we apply simulation optimization to narrow the reality gap. Our neural network-based policies use only onboard sensor data and run entirely on the embedded drone hardware. In extensive real-world experiments, we compare three different control structures ranging from low-level pulse-width-modulated motor commands to high-level attitude control based on nested proportional-integral-derivative controllers. Our experiments show that low-level controllers trained with reinforcement learning require a more accurate simulation than higher-level control policies.