Explanations are central to improving transparency, trust, and user satisfaction in recommender systems (RS), yet it remains unclear how different explanation formats (visual vs. textual) are suited to users with different personal characteristics (PCs). To this end, we report a within-subject user study (n=54) comparing visual and textual explanations and examine how explanation format and PCs jointly influence perceived control, transparency, trust, and satisfaction in an educational recommender system (ERS). Using robust mixed-effects models, we analyze the moderating effects of a wide range of PCs, including Big Five traits, need for cognition, decision making style, visualization familiarity, and technical expertise. Our results show that a well-designed visual, simple, interactive, selective, easy to understand visualization that clearly and intuitively communicates how user preferences are linked to recommendations, fosters perceived control, transparency, appropriate trust, and satisfaction in the ERS for most users, independent of their PCs. Moreover, we derive a set of guidelines to support the effective design of explanations in ERSs.

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