Although the capabilities of automated driving systems (ADS) are growing, the human operator remains in charge of driving the vehicle outside the operational design domain and after requests to intervene. The vehicle sensors required for ADS and new regulation for driver availability monitoring systems stimulate the development of systems that can monitor human driving ability. Such systems could allow for ADS to track possible driving skill degradation, monitor driver impairment, or adapt to the driver’s needs. However, knowledge is required about how to assess human driving ability effectively. This work proposes a novel method to capture driving skill and style based on curve driving, straight-road driving, and driving through road narrowings. In addition to conventional measures, the study introduces new measures, including the relationship between steering angle and eye movements. Employing a high-fidelity simulator, we compared the vehicle-control-related measures (i.e., driving skill measures), trajectory-planning and speed-related measures (i.e., driving style measures), and eye movements of sixteen inexperienced and thirteen experienced drivers. It was examined which of these measures are valid, i.e., allow a statistical discrimination between experienced and inexperienced drivers. The study was complemented with two expert drivers serving as a benchmark. The results showed that the experienced drivers adopted a more abrupt braking style when approaching curves and a higher speed through the different track sections than the inexperienced drivers. No statistically significant differences were observed between the skill measures of the experienced and inexperienced drivers. An analysis of lead times obtained through a cross-correlation between horizontal gaze angle and steering angle showed that eye movements generally preceded steering movements. However, differences in lead times between experienced and inexperienced drivers were not statistically significant, which may have been caused by eye-tracking measurement inaccuracies, the layout of the driving task and strong intra-individual variability in looking behavior. The eye-tracking results of the road-narrowings showed that the experienced and inexperienced drivers reduced their vertical gaze dispersion, while only the experienced drivers statistically significantly reduced their horizontal gaze dispersion compared to the straights. In other words, the experienced drivers showed increased horizontal gaze tunneling from the straights to the narrowings, while the inexperienced drivers only showed vertical gaze tunneling. The results of the expert drivers showed consistent higher speed, lower control activity, and more of a racing line through the curves than the experienced and inexperienced drivers. Furthermore, the results showed that the expert drivers adopted a more variable horizontal gaze strategy between different curves. Overall, these results indicate that driving style and eye-movement measures, but not driving skill measures, allow differentiating between experienced and inexperienced drivers using a driving simulator. These findings may be explained by the fact that driving is a self-paced task, i.e., more competent drivers increase their own task demands by driving faster. Future research could examine how strongly scores the present driving and eye-movement measures correlate with drivers’ take-over quality in automated driving scenarios.