Parkinson's disease (PD) is a progressive neurodegenerative disorder that, in addition to directly impairing functional mobility, is frequently associated with vocal impairments such as hypophonia and dysarthria, which typically manifest in the early stages. The use of vocal biomarkers to support the early diagnosis of PD presents a non-invasive, low-cost, and accessible alternative in clinical settings. Thus, the objective of this cross-sectional study was to consistently evaluate the effectiveness of a Deep Neural Network (DNN) in distinguishing individuals with Parkinson's disease from healthy controls, in comparison with traditional Machine Learning (ML) methods, using vocal biomarkers. Two publicly available voice datasets were used. Mel-frequency cepstral coefficients (MFCCs) were extracted from the samples, and model robustness was assessed using a validation strategy with 1000 independent random executions. Performance was evaluated using classification statistics. Since normality assumptions were not satisfied, non-parametric tests (Kruskal-Wallis and Bonferroni post-hoc tests) were applied to verify whether the tested classification models were similar or different in the classification of PD. With an average accuracy of $98.65\%$ and $92.11\%$ on the Italian Voice dataset and Parkinson's Telemonitoring dataset, respectively, the DNN demonstrated superior performance and efficiency compared to traditional ML models, while also achieving competitive results when benchmarked against relevant studies. Overall, this study confirms the efficiency of DNNs and emphasizes their potential to provide greater accuracy and reliability for the early detection of neurodegenerative diseases using voice-based biomarkers.