Researchers have debated whether instructional-based teaching or exploration-based active learning is better for decades with unsatisfying results. A main obstacle is the difficulty in precisely controlling and characterizing the pedagogical methods used and the learning conditions in empirical studies. To address this, we leveraged existing computational models of teaching and active learning to formalize the methods and the learning process. We compared the two pedagogical methods in a concept-learning framework and investigated their effectiveness under various scenarios. Our results show that when the learner and teacher are conceptually aligned, teaching is at least as effective as, and often much more effective than active learning, but when the alignment is broken, active learning can yield moderate improvement over teaching. We conclude by discussing our results' implications for the debate and the prospects of bringing computational models to bear on complex real-world problems that are resistant to simple experimental investigation.