The aim of this study was to compare the performance of two bivariate visualizations by measuring response correctness (error rate) and response time, and to identify the differences in cognitive processes involved in map-reading tasks by using eye-tracking methods. The present study is based on our previous research and the hypothesis that the use of different visualization methods may lead to significant cognitive-processing differences. We applied extrinsic and intrinsic visualizations in the study. Participants in the experiment were presented maps which depicted two variables (soil moisture and soil depth) and asked to identify the areas which displayed either a single condition (e.g., "find an area with low soil depth") or both conditions (e.g., "find an area with high soil moisture and low soil depth"). The research sample was composed of 31 social sciences and humanities university students. The experiment was performed under laboratory conditions, and Hypothesis software was used for data collection. Eye-tracking data were collected for 23 of the participants. An SMI RED-m eye-tracker was used to determine whether either of the two visualization methods was more efficient for solving the given map-reading tasks. Our results showed that with the intrinsic visualization method, the participants spent significantly more time with the map legend. This result suggests that extrinsic and intrinsic visualizations induce different cognitive processes. The intrinsic method was observed to generally require more time and led to higher error rates. In summary, the extrinsic method was found to be more efficient than the intrinsic method, although the difference was less pronounced in the tasks which contained two variables, which proved to be better suited to intrinsic visualization.