Stress and cognitive overload during driving are associated with decreased performance potentially leading to serious mistakes and even fatal incidents. Therefore, research on drivers’ mental states recognition is promising to reduce these traffic accidents caused by human error (e.g., in combination with driver assistance systems and automated driving functions). Easy-to-use, unobtrusive wearables allow convenient measurement of electrodermal activity (EDA) which is an informative measure for the experienced stress level. In this article, we explore the potential of various conventional machine learning (ML) models with hand-crafted features, automated pipeline optimization (AutoML), and deep learning (DL) to recognize drivers’ stress states from EDA recordings in a driving simulator. Three different stress states (low, mid, and high stress) were induced via (a) the complexity level of the driving task (manual and automated driving) and (b) simultaneous secondary cognitive tasks. Our results reveal that a k-nearest neighbors (KNN) classifier with handcrafted features of the phasic and tonic EDA response as well as a pipeline suggested by AutoML via Tree-Based Pipeline Optimization (TPOT) are particularly suited with a high classification performance above an empirical chance level estimated via a dummy classifier. Our results propose that AutoML might be beneficial to find optimal ML pipelines for EDA-based state recognition. In the future, we aim to evaluate the here proposed models regarding their generalization ability by applying them (a) on new datasets collected during realistic driving scenarios and (b) within a subject-independent approach (i.e., training one model for all subjects).