In recent decades, the incidence of melanoma has grown rapidly. Hence, early diagnosis is crucial to improving clinical outcomes. Here, we propose and compare a classical image analysis-based machine learning method with a deep learning one to automatically classify benign vs. malignant dermoscopic skin lesion images. The same dataset of 25,122 publicly available dermoscopic images was used to train both models, while a disjointed test set of 200 images was used for the evaluation phase. The training dataset was randomly divided into 10 datasets of 19,932 images to obtain an equal distribution between the two classes. By testing both models on the disjoint set, the deep learning-based method returned accuracy of 85.4 ± 3.2% and specificity of 75.5 ± 7.6%, while the machine learning one showed accuracy and specificity of 73.8 ± 1.1% and 44.5 ± 4.7%, respectively. Although both approaches performed well in the validation phase, the convolutional neural network outperformed the ensemble boosted tree classifier on the disjoint test set, showing better generalization ability. The integration of new melanoma detection algorithms with digital dermoscopic devices could enable a faster screening of the population, improve patient management, and achieve better survival rates.