Mobile face recognition has become increasingly important, especially during the COVID-19 pandemic when the use of masks has become ubiquitous. The area that can be analyzed for face recognition is narrowed down only to the periocular area. This resulted in many studies of face recognition in the periocular area which require appropriate datasets, one of which is M2FRED, introduced by University of Salerno. Previous research on M2FRED using supervised learning algorithms such as Support Vector Machine (SVM), Multilayer Perceptron (MLP), Random Forest (RF), and Decision Tree (DT) shows promising results on M2FRED with accuracy at 95.4% using MLP. However, study on M2FRED using deep learning models has yet to be done. In this paper, we compare the performance of MobileNet and Siamese neural networks on M2FRED, a face dataset specifically designed for mobile face recognition that contains videos of 43 subjects with and without masks taken in uncontrolled environments using mobile devices. We employ this range of M2FRED to evaluate the performance of MobileNet and Siamese neural networks in handling challenges like face masks, various lighting conditions, and limited computational resources. MobileNet outperformed the Siamese neural network in every aspect with an average accuracy score of 99.77% for overall performance (99.85%), mask usage scenarios (100%), and lighting context (99.72% for indoor evaluation and 99.52% for outdoor evaluation). With its simple architecture, MobileNet also surpassed Siamese neural networks in terms of complexity.