Machine learning (ML) is widely used today, especially through deep neural networks (DNNs), however, increasing computational load and resource requirements have led to cloud-based solutions. To address this problem, a new generation of networks called Spiking Neural Networks (SNN) has emerged, which mimic the behavior of the human brain to improve efficiency and reduce energy consumption. These networks often process large amounts of sensitive information, such as confidential data, and thus privacy issues arise. Homomorphic encryption (HE) offers a solution, allowing calculations to be performed on encrypted data without decrypting it. This research compares traditional DNNs and SNNs using the Brakerski/Fan-Vercauteren (BFV) encryption scheme. The LeNet-5 model, a widely-used convolutional architecture, is used for both DNN and SNN models based on the LeNet-5 architecture, and the networks are trained and compared using the FashionMNIST dataset. The results show that SNNs using HE achieve up to 40% higher accuracy than DNNs for low values of the plaintext modulus t, although their execution time is longer due to their time-coding nature with multiple time-steps.