Using simulation-based inference (SBI), such as randomization tests, as the primary vehicle for introducing students to the logic and scope of statistical inference has been advocated with the potential of improving student understanding of statistical inference and the statistical investigative process. Moving beyond the individual class activity, entirely revised introductory statistics curricula centering on these ideas have been developed and tested. Preliminary assessment data have been mostly positive. In this paper, we discuss three years of cross-institutional tertiary-level data from the United States comparing SBI-focused curricula and non-SBI curricula (86 distinct institutions). We examined several pre/post measures of conceptual understanding in the introductory algebra-based course using multi-level modelling to incorporate student-level, instructor-level, and institutional-level covariates. We found that pre-course student characteristics (e.g., prior knowledge) were the strongest predictors of student learning, but also that textbook choice can still have a meaningful impact on student understanding of key statistical concepts. In particular, textbook choice was the strongest "modifiable" predictor of student outcomes of those examined, with simulation-based inference texts yielding the largest improvements in student learning outcomes. Further research is needed to elucidate the aspects of SBI curricula that contribute to observed student learning gains.