Pedestrians rely on vehicle dynamics, engine sound, and driver cues. The lack of engine sound now constitutes an addressed pedestrian safety issue for (hybrid) electric vehicles ((H)EVs). Analogously, lacking driver cues may constitute a pedestrian safety issue for self-driving vehicles (SDVs). The purpose of this study was to systematically compare the relevance of substituting driver cues with an external human-machine interface among SDVs (no eHMI vs. eHMI) with the relevance of substituting engine sound with artificial sound among (H)EVs (no engine sound vs. engine sound). In a within-subject design, twenty-nine participants acting as pedestrians encountered a simulated SDV in a parking lot. The results revealed that both informational cues have equally large effects on subjective measures such as perceived safety. In semi-structured interviews, participants stated that it is equally crucial to equip SDVs with an eHMI as equipping (H)EVs with an artificial sound generator. We conclude that an eHMI for SDVs seems to be as relevant as an artificial sound for (H)EVs.