This article presents a solution to intercept an agile drone by another agile drone carrying a catching net. We formulate the interception as a Competitive Reinforcement Learning problem, where the interceptor and the target drone are controlled by separate policies trained with Proximal Policy Optimization (PPO). We introduce a high-fidelity simulation environment that integrates a realistic quadrotor dynamics model and a low-level control architecture implemented in JAX, which allows for fast parallelized execution on GPUs. We train the agents using low-level control, collective thrust and body rates, to achieve agile flights both for the interceptor and the target. We compare the performance of the trained policies in terms of catch rate, time to catch, and crash rate, against common heuristic baselines and show that our solution outperforms these baselines for interception of agile targets. Finally, we demonstrate the performance of the trained policies in a scaled real-world scenario using agile drones inside an indoor flight arena.