Collaborative robots (cobots) have largely replaced conventional industrial robots in today’s workplaces, particularly in manufacturing setups, due to their improved performance and intelligent design. In the framework of Industry 5.0, humans are working alongside cobots to accomplish the required level of automation. However, human–robot interaction has brought up concerns regarding human factors (HF) and ergonomics. A human worker may experience cognitive stress as a result of cobots’ irresponsive nature in unpredictably occurring situations, which adversely affects productivity. Therefore, there is a necessity to measure stress to enhance a human worker’s performance in a human–robot collaborative environment. In this study, factory workers’ mental workload was assessed using physiological, behavioural, and subjective measures. Electroencephalography (EEG) and functional near-infrared spectroscopy (fNIRS) signals were collected to acquire brain signals and track hemodynamic activity, respectively. The effect of task complexity, cobot movement speed, and cobot payload capacity on the mental stress of a human worker were observed for a task designed in the context of a smart factory. Task complexity and cobot speed proved to be more impactful. As physiological measures are unbiased and more authentic means to estimate stress, eventually they may replace the other conventional measures if they prove to correlate with the results of traditional ones. Here, regression and artificial neural networks (ANN) were utilised to determine the correlation between physiological data and subjective and behavioural measures. Regression performed better for most of the targets and the best correlation (rsq-adj = 0.654146) was achieved for predicting missed beeps, a behavioural measure, using a combination of multiple EEG and fNIRS predictors. The k-nearest neighbours (KNN) algorithm was used to evaluate the accuracy of correlation between traditional measures and physiological variables, with the highest accuracy of 77.8% achieved for missed beeps as the target. Results show that physiological measures can be more insightful and have the tendency to replace other biased parameters.