The sample inefficiency of reinforcement learning (RL) remains a significant challenge in robotics. RL requires large-scale simulation and can still cause long training times, slowing research and innovation. This issue is particularly pronounced in vision-based control tasks where reliable state estimates are not accessible. Differentiable simulation offers an alternative by enabling gradient back-propagation through the dynamics model, providing low-variance analytical policy gradients and, hence, higher sample efficiency. However, its usage for real-world robotic tasks has yet been limited. This work demonstrates the great potential of differentiable simulation for learning quadrotor control. We show that training in differentiable simulation significantly outperforms model-free RL in terms of both sample efficiency and training time, allowing a policy to learn to recover a quadrotor in seconds when providing vehicle states and in minutes when relying solely on visual features. The key to our success is two-fold. First, the use of a simple surrogate model for gradient computation greatly accelerates training without sacrificing control performance. Second, combining state representation learning with policy learning enhances convergence speed in tasks where only visual features are observable. These findings highlight the potential of differentiable simulation for real-world robotics and offer a compelling alternative to conventional RL approaches.