The emergence of brain-inspired neuromorphic computing as a paradigm for edge AI is motivating the search for high-performance and efficient spiking neural networks to run on this hardware. However, compared to classical neural networks in deep learning, current spiking neural networks lack competitive performance in compelling areas. Here, for sequential and streaming tasks, we demonstrate how spiking recurrent neural networks (SRNN) using adaptive spiking neurons are able to achieve state-of-the-art performance compared to other spiking neural networks and almost reach or exceed the performance of classical recurrent neural networks (RNNs) while exhibiting sparse activity. From this, we calculate a 100x energy improvement for our SRNNs over classical RNNs on the harder tasks. We find in particular that adapting the timescales of spiking neurons is crucial for achieving such performance, and we demonstrate the performance for SRNNs for different spiking neuron models.