Spiking Neural Networks (SNNs) event-driven nature enables efficient encoding of spatial and temporal features, making them suitable for dynamic time-dependent data processing. Despite their biological relevance, SNNs have seen limited application in medical image recognition due to difficulties in matching the performance of conventional deep learning models. To address this, we propose a novel breast cancer classification approach that combines SNNs with Lempel-Ziv Complexity (LZC) a computationally efficient measure of sequence complexity. LZC enhances the interpretability and accuracy of spike-based models by capturing structural patterns in neural activity. Our study explores both biophysical Leaky Integrate-and-Fire (LIF) and probabilistic Levy-Baxter (LB) neuron models under supervised, unsupervised, and hybrid learning regimes. Experiments were conducted on the Breast Cancer Wisconsin dataset using numerical features derived from medical imaging. LB-based models consistently exceeded 90.00% accuracy, while LIF-based models reached over 85.00%. The highest accuracy of 98.25% was achieved using an ANN-to-SNN conversion method applied to both neuron models comparable to traditional deep learning with back-propagation, but at up to 100 times lower computational cost. This hybrid approach merges deep learning performance with the efficiency and plausibility of SNNs, yielding top results at lower computational cost. We hypothesize that the synergy between temporal-coding, spike-sparsity, and LZC-driven complexity analysis enables more-efficient feature extraction. Our findings demonstrate that SNNs combined with LZC offer promising, biologically plausible alternative to conventional neural networks in medical diagnostics, particularly for resource-constrained or real-time systems.