When designing a car, the vehicle dynamics and handling are important aspects, as they can satisfy a purpose in professional racing, as well as contributing to driving pleasure and safety, real and perceived, in regular drivers. In this paper, we focus on the assessment of the emotional response in drivers while they are driving on a track with different car handling setups. The experiments were performed using a dynamic professional simulator prearranged with different car setups. We recorded various physiological signals, allowing us to analyze the response of the drivers and analyze which car setup is more influential in terms of stress arising in the subjects. We logged two skin potential responses (SPRs), the electrocardiogram (ECG) signal, and eye tracking information. In the experiments, three car setups were used (neutral, understeering, and oversteering). To evaluate how these affect the drivers, we analyzed their physiological signals using two statistical tests (t-test and Wilcoxon test) and various machine learning (ML) algorithms. The results of the Wilcoxon test show that SPR signals provide higher statistical significance when evaluating stress among different drivers, compared to the ECG and eye tracking signals. As for the ML classifiers, we count the number of positive or “stress” labels of 15 s SPR time intervals for each subject and each particular car setup. With the support vector machine classifier, the mean value of the number of positive labels for the four subjects is equal to 13.13% for the base setup, 44.16% for the oversteering setup, and 39.60% for the understeering setup. In the end, our findings show that the base car setup appears to be the least stressful, and that our system enables us to effectively recognize stress while the subjects are driving in the different car configurations.