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Two spacecraft charging software tools, the Spacecraft Plasma Interaction Software and the Multi-Utility Spacecraft Charging Analysis Tool, have been compared in the situation of a wake generated by an object immersed in dense drifting plasma. Each model takes account of the particle dynamics, the space charge effect on the electric field, and the currents collected by the object. The cross-comparison resulted in a good agreement between the two codes and with previous experiments conducted on the same configuration. In particular, a highly negative voltage imposed to the object rear side allows the collection of drifting ions at this location. The nontrivial shape of the current density map was correctly simulated by the two codes. Future works may allow to reach a better quantitative agreement.