Argumentation is crucial for all academic disciplines. Nevertheless, a lack of argumentation skills among students is evident. Two core aspects of argumentation are the recognition of argument structures (e.g., backing up claims with premises, according to the Toulmin model) and the recognition of fallacies. As both aspects may be related to content knowledge, students studying different subjects might exhibit different argumentation skills depending on whether the content is drawn from their own or from a foreign subject. Therefore, we developed an instrument to measure the recognition of both argument structures and fallacies among the groups of preservice teachers and business economics students in both their respective domains (pedagogy and economics), and a neutral domain (sustainability). For the recognition of fallacies, we distinguished between congruent and incongruent fallacies. In congruent fallacies, the two aspects of argument quality, i.e., deductive validity and inductive strength, provide converging evidence against high argument quality. In incongruent fallacies, these two aspects diverge. Based on dual process theories, we expected to observe differences in the recognition of congruent and incongruent fallacies. We investigated whether these two abilities are domain-specific and whether the recognition of fallacies depends on the congruence of two aspects of argument quality. 267 preservice teachers and 56 business economics students participated in the study. For the recognition of argument structures, participants assigned the five statements constituting one argument to the corresponding component according to the Toulmin model. For the recognition of fallacies, we created arguments and incorporated a common fallacy into some of them: formal fallacy, overgeneralization, irrelevance, or circularity. Participants rated whether the argument was cogent or not, which was followed by a brief justification. Domain specificity could not be found for either of both abilities. For the recognition of fallacies, two dimensions were found: a congruent dimension (formal fallacies and overgeneralizations) and an incongruent dimension (irrelevance and circularity). The instrument measures the recognition of both argument structures and fallacies in these two groups across domains. The recognition of fallacies differs depending on whether the deductive validity and the inductive strength of the argument are equally indicative of argument quality or not.