Counterfactual explanations (CFEs) are a popular approach in explainable artificial intelligence (xAI), highlighting changes to input data necessary for altering a model's output. A CFE can either describe a scenario that is better than the factual state (upward CFE), or a scenario that is worse than the factual state (downward CFE). However, potential benefits and drawbacks of the directionality of CFEs for user behavior in xAI remain unclear. The current user study (N=161) compares the impact of CFE directionality on behavior and experience of participants tasked to extract new knowledge from an automated system based on model predictions and CFEs. Results suggest that upward CFEs provide a significant performance advantage over other forms of counterfactual feedback. Moreover, the study highlights potential benefits of mixed CFEs improving user performance compared to downward CFEs or no explanations. In line with the performance results, users' explicit knowledge of the system is statistically higher after receiving upward CFEs compared to downward comparisons. These findings imply that the alignment between explanation and task at hand, the so-called regulatory fit, may play a crucial role in determining the effectiveness of model explanations, informing future research directions in xAI. To ensure reproducible research, the entire code, underlying models and user data of this study is openly available: https://github.com/ukuhl/DirectionalAlienZoo