The demand for autonomous flight of drones in complex dynamic environments is increasing. However, addressing the challenges posed by dynamic obstacles in such environments remains highly challenging for perception systems. Traditional frame-based cameras suffer from motion blur in high dynamic scenes, resulting in degraded image quality and inaccurate object detection, which may subsequently affect obstacle avoidance and pose safety concerns for flight. To tackle this issue, we propose a novel bio-inspired visual sensor, namely event camera or dynamic vision sensor (DVS), for dynamic object detection in complex scenes. We present two object detection frameworks based on different event processing methods for two types of event cameras currently available: motion-compensated average timestamp image-based object detection and event accumulation image-based object detection. Furthermore, we design a fusion scheme for integrating event-based detection results with standard frame-based detection results based on whether the event camera is capable of outputting standard frames. Our approach successfully integrates the accuracy of object detection by standard frame cameras in relatively static environments with the robustness of event cameras in dynamic scenes, while addressing the issue of poor object detection by standard frames in dark environments due to extremely low image quality.