Brain-inspired computing continues to advance in an ongoing process focusing on enhancing machine intelligence via models that emulate cognitive processes. The study provides a comparative study of liquid state machines (LSMs) and spiking neural networks (SNNs) on image classification, using the MNIST and KTH action detection databases. The first section points to the improvement of LSMs through an evolutionary membrane algorithm that seeks to optimize neural architecture and hyperparameter settings. The experimental results show that the optimized LSM realizes a 92.22% accuracy on the MNIST dataset, in addition to a precision of 92.41%, a recall rate of 92.20%, and an F1-score of 92.19%. With respect to the KTH dataset, the LSM realized an accuracy of 89.85%, complemented by a precision of 90.08%, a recall of 89.88%, and an F1-score of 89.89%. The second section provides an SNN enhanced by spike frequency adaptation (SFA), which includes dynamic firing thresholds to promote adaptability and general performance. The specific model achieves a 95.60% accuracy on the MNIST dataset, realizing a precision of 95.12%, a recall of 94.39%, and an F1-score of 94.75%. With respect to the KTH dataset, the SNN achieved an accuracy of 84.69%, complemented by a precision of 85.85%, a recall of 84.69%, and an F1-score of 84.40%. This research shows the ability of LSMs and SNNs in advancing image classification methods, hence impacting the broader areas of deep learning and neuromorphic computing.