The baroreflex is one of the most important control mechanisms in the human cardiovascular system. This work utilises a closed-loop in silico model of baroreflex regulation, coupled to pulsatile mechanical models with (i) one heart chamber and 36-parameters and (ii) four chambers and 51 parameters. We perform the first global sensitivity analysis of these closed-loop systems which considers both cardiovascular and baroreflex parameters, and compare the models with their respective unregulated equivalents. Results show the reduced influence of regulated parameters compared to unregulated equivalents and that, in the physiological resting state, model outputs (pressures, heart rate, cardiac output etc.) are most sensitive to parasympathetic arc parameters. This work provides insight into the effects of regulation and model input parameter influence on clinical metrics, and constitutes a first step to understanding the role of regulation in models for personalised healthcare.