In this paper, five strategies for controlling the negative sequence currents of a Virtual Synchronous Machine (VSM) under unbalanced conditions are comparatively assessed, considering both grid-connected and islanded operation. While these strategies have been individually proposed in recent literature, their characteristics and performance have not previously been systematically evaluated. Thus, a VSM structure serving as basis for the comparison is presented in detail, with modifications for preventing double frequency power oscillations from influencing the virtual swing equation and the inertial dynamics. The active and reactive power oscillations, and the power transfer capability within the converter current limitation, are theoretically derived as a function of the unbalances in the local voltage. Simulation results and experimental validation on a 50 kVA Modular Multilevel Converter (MMC) prototype with 12 sub-modules per arm demonstrate the validity of the theoretical analysis. The presented results serve as basis for evaluating the applicability of the studied control strategies under different operating conditions.