Recent research has shown that smartphones/smartwatches have a high potential to help physicians to identify and differentiate between different movement disorders. This work aims to develop Machine Learning models to improve the differential diagnosis between patients with Parkinson's Disease and Essential Tremor. For this purpose, we use a mobile phone's built-in gyroscope to record the angular velocity signals of two different arm positions during the patient's follow-up, more precisely, in rest and posture positions. To develop and to find the best classification models, diverse factors were considered, such as the frequency range, the training and testing divisions, the kinematic features, and the classification method. We performed a two-stage kinematic analysis, first to differentiate between healthy and trembling subjects and then between patients with Parkinson's Disease and Essential Tremor. The models developed reached an average accuracy of 97.2 ± 3.7% (98.5% Sensitivity, 93.3% Specificity) to differentiate between Healthy and Trembling subjects and an average accuracy of 77.8 ± 9.9% (75.7% Sensitivity, 80.0% Specificity) to discriminate between Parkinson's Disease and Essential Tremor patients. Therefore, we conclude, that the angular velocity signal can be used to develop Machine Learning models for the differential diagnosis of Parkinson's disease and Essential Tremor.