As machine learning models increasingly process sensitive data, understanding their vulnerability to privacy attacks is vital. Membership inference attacks (MIAs) exploit model responses to infer whether specific data points were used during training, posing a significant privacy risk. Prior research suggests that spiking neural networks (SNNs), which rely on event-driven computation and discrete spike-based encoding, exhibit greater resilience to MIAs than artificial neural networks (ANNs). This resilience stems from their non-differentiable activations and inherent stochasticity, which obscure the correlation between model responses and individual training samples. To enhance privacy in SNNs, we explore two techniques: quantization and surrogate gradients. Quantization, which reduces precision to limit information leakage, has improved privacy in ANNs. Given SNNs' sparse and irregular activations, quantization may further disrupt the activation patterns exploited by MIAs. We assess the vulnerability of SNNs and ANNs under weight and activation quantization across multiple datasets, using the attack model's receiver operating characteristic (ROC) curve area under the curve (AUC) metric, where lower values indicate stronger privacy, and evaluate the privacy-accuracy trade-off. Our findings show that quantization enhances privacy in both architectures with minimal performance loss, though full-precision SNNs remain more resilient than quantized ANNs. Additionally, we examine the impact of surrogate gradients on privacy in SNNs. Among five evaluated gradients, spike rate escape provides the best privacy-accuracy trade-off, while arctangent increases vulnerability to MIAs. These results reinforce SNNs' inherent privacy advantages and demonstrate that quantization and surrogate gradient selection significantly influence privacy-accuracy trade-offs in SNNs.