Instructional physics labs offer students unique opportunities to develop an understanding of experimentation. By transforming labs to be more open ended and experimentation focused, instructors can better support student agency and choice. In this study, we examine students’ overall sense of and perceptions about agency in two experimentation-focused labs: one course primarily taken by physics majors and another course primarily taken by engineering majors. We compare the sense of and perceptions about agency between the different courses and between men and women in each course. Between the start and the end of the semester, we found a positive shift in students’ sense of agency in the lab activities in both courses, with no difference between men’s and women’s shifts. Additionally, we found empirical evidence that the majority of the students preferred the final, most open-ended Project lab. Our qualitative analysis revealed that most of the students perceived the opportunities for agency positively, citing “freedom” as their reason for preferring the Project lab. Both women and men in the course for engineering majors showed similar patterns. Fewer women in the physics majors course, however, chose the final project lab as their favorite and less often attributed their preference to freedom. We discuss possible interpretations of these results and implications for instruction. © 2021 Published by the American Physical Society