Traumatic Brain Injury (TBI) and stroke are devastating neurological conditions that affect hundreds of people daily. Unfortunately, detecting TBI and stroke without specific imaging techniques or access to a hospital often proves difficult. Our prior research used machine learning on electroencephalograms (EEGs) to select important features and to classify between normal, TBI, and stroke on an independent dataset from a public repository with an accuracy of 0.71. In this study, we expanded to explore whether featureless and deep learning models can provide better performance in distinguishing between TBI, stroke and normal EEGs by including more comprehensive data extraction tools to drastically increase the size of the training dataset. We compared the performance of models built upon selected features with Linear Discriminative Analysis and ReliefF with several featureless deep learning models. We achieved 0.85 area under the curve (AUC) of the receiver operating characteristic curve (ROC) using feature-based models, and 0.84 AUC with featureless models. In addition, we demonstrated that Gradient-weighted Class Activation Mapping (Grad-CAM) can provide insight into patient-specific EEG classification by highlighting problematic EEG segments during clinical review. Overall, our study suggests that machine learning and deep learning of EEG or its precomputed features can be a useful tool for TBI and stroke detection and classification. Although not surpassing the performance of feature-based models, featureless models reached similar levels without prior computation of a large feature set allowing for faster and cost-efficient deployment, analysis, and classification.