Side-Channel Attacks, are a prominent type of attacks, used to break cryptographic implementations on a computing system. They are based on information "leaked" by the hardware of a computing system, rather than the encryption algorithm itself. Recent studies showed that Side-Channel Attacks can be performed using Deep Learning models. In this study, we examine the performance of Convolutional Neural Networks, on four different datasets of side- channel data and we compare our models with conventional Machine Learning algorithms and a CNN model from literature. We found that CNNs have the potential to achieve high accuracy performance (99.8%), although their capacity is heavily influenced by the use case. We also found that certain Machine Learning algorithms can outperform CNNs in certain cases, leaving an open debate on the performance gains of the latter.