In high-speed quadcopter racing, finding a single controller that works well across different platforms remains challenging. This work presents the first neural network controller for drone racing that generalizes across physically distinct quadcopters. We demonstrate that a single network, trained with domain randomization, can robustly control various types of quadcopters. The network relies solely on the current state to directly compute motor commands. The effectiveness of this generalized controller is validated through real-world tests on two substantially different crafts (3-inch and 5-inch race quadcopters). We further compare the performance of this generalized controller with controllers specifically trained for the 3-inch and 5-inch drone, using their identified model parameters with varying levels of domain randomization (0%, 10%, 20%, 30%). While the generalized controller shows slightly slower speeds compared to the fine-tuned models, it excels in adaptability across different platforms. Our results show that no randomization fails sim-to-real transfer while increasing randomization improves robustness but reduces speed. Despite this trade-off, our findings highlight the potential of domain randomization for generalizing controllers, paving the way for universal AI controllers that can adapt to any platform.