Recently, we have proposed a body-sensor-network-based approach, composed of a few body-worn wireless inertial nodes, for automatic assignment of Unified Parkinson's Disease Rating Scale (UPDRS) scores in the following tasks: Leg agility (LA), Sit-to-Stand (S2S), and Gait (G). Unlike our previous works and the majority of the published studies, where UPDRS tasks were the sole focus, in this paper, we carry out a comparative investigation of the LA, S2S, and G tasks. In particular, after providing an accurate description of the features identified for the kinematic characterization of the three tasks, we comment on the correlation between the most relevant kinematic parameters and the UPDRS scoring. We analyzed the performance achieved by the automatic UPDRS scoring system and compared the estimated UPDRS evaluation with the one performed by neurologists, showing that the proposed system compares favorably with typical interrater variability. We then investigated the correlations between the UPDRS scores assigned to the various tasks by both the neurologists and the automatic system. The results, based on a limited number of subjects with Parkinson's disease (PD) (34 patients, 47 clinical trials), show poor-to-moderate correlations between the UPDRS scores of different tasks, highlighting that the patients' motor performance may vary significantly from one task to another, since different tasks relate to different aspects of the disease. An aggregate UPDRS score is also considered as a concise parameter, which can provide additional information on the overall level of the motor impairments of a Parkinson's patient. Finally, we discuss a possible implementation of a practical e-health application for the remote monitoring of PD patients.