Since Helicon plasma sources can efficiently couple power and generate high-density plasma, they have received interest also as spacecraft propulsive devices, among other applications. In order to maximize the power deposited into the plasma, it is necessary to assess the performance of the radiofrequency (RF) antenna that drives the discharge, as typical plasma parameters (e.g., the density) are varied. For this reason, we have conducted a comparative analysis of three Helicon sources which feature different RF antennas, namely, the single-loop, the Nagoya Type-III, and the Fractional helix. These antennas are compared in terms of input impedance and induced current density; in particular, the real part of the impedance constitutes a measure of the antenna ability to couple power into the plasma. The results presented in this work have been obtained through a full-wave approach which (being hinged on the numerical solution of a system of integral equations) allows computing the antenna current and impedance self-consistently. Our findings indicate that certain combinations of plasma parameters can indeed maximize the real part of the input impedance and, thus, the deposited power, and that one of the three antennas analyzed performs best for a given plasma. Furthermore, unlike other strategies which rely on approximate antenna models, our approach enables us to reveal that the antenna current density is not spatially uniform, and that a correlation exists between the plasma parameters and the spatial distribution of the current density.