Spiking neural networks coupled with neuromorphic hardware and event-based sensors are getting increased interest for low-latency and low-power inference at the edge. However, multiple spiking neuron models have been proposed in the literature with different levels of biological plausibility and different computational features and complexities. Consequently, there is a need to define the right level of abstraction from biology in order to get the best performance in accurate, efficient and fast inference in neuromorphic hardware. In this context, we explore the impact of synaptic and membrane leakages in spiking neurons. We confront three neural models with different computational complexities using feedforward and recurrent topologies for event-based visual and auditory pattern recognition. Our results show that, in terms of accuracy, leakages are important when there are both temporal information in the data and explicit recurrence in the network. In addition, leakages do not necessarily increase the sparsity of spikes flowing in the network. We also investigate the impact of heterogeneity in the time constant of leakages, and the results show a slight improvement in accuracy when using data with a rich temporal structure. These results advance our understanding of the computational role of the neural leakages and network recurrences, and provide valuable insights for the design of compact and energy-efficient neuromorphic hardware for embedded systems.