Event-based sensors, with their high temporal resolution (1us) and dynamical range (120dB), have the potential to be deployed in high-speed platforms such as vehicles and drones. However, the highly sparse and fluctuating nature of events poses challenges for conventional object detection techniques based on Artificial Neural Networks (ANNs). In contrast, Spiking Neural Networks (SNNs) are well-suited for representing event-based data due to their inherent temporal dynamics. In particular, we demonstrate that the membrane potential dynamics can modulate network activity upon fluctuating events and strengthen features of sparse input. In addition, the spike-triggered adaptive threshold can stabilize training which further improves network performance. Based on this, we develop an efficient spiking feature pyramid network for event-based object detection. Our proposed SNN outperforms previous SNNs and sophisticated ANNs with attention mechanisms, achieving a mean average precision (map50) of 47.7% on the Gen1 benchmark dataset. This result significantly surpasses the previous best SNN by 9.7% and demonstrates the potential of SNNs for event-based vision. Our model has a concise architecture while maintaining high accuracy and much lower computation cost as a result of sparse computation. Our code will be publicly available.