This study investigated students' peer discussions on quantum physics questions administered via an electronic response system. Participants in an undergraduate-level quantum physics course for science teacher candidates and a modern physics course for physics and physics teacher education students answered 51 quantum physics questions in two rounds (an individual round and a group round with peers) over six sessions throughout the semester. The analysis focused on changes in group round mean percentages of correct answers by Bloom Taxonomy levels and quantum physics subjects, as well as the reported benefits of peer discussions. The results demonstrated that while peer discussions statistically improved correct responses for both groups, the impact varied between physics-oriented students and science teacher education students with less physics background. Explained benefits about peer discussions pointed out some differences between the cases.