The construction of the double first-class university is significant in China's higher education. However, the question of whether students' abilities are better developed at double first-class universities remains unanswered. Based on data from the 2019 Shaanxi University Graduates' Employment and Entrepreneurship Quality Tracking Survey, we categorized universities into double first-class and non-double first-class. This study examined the effect mechanism of institution type on students' ability development using propensity score matching and student engagement's mediating effect on this relationship using the bootstrap estimation. The results demonstrated that students at double first-class universities exhibited significantly better core skills, research capabilities, and self-awareness and globalization abilities than those at non-double first-class universities. The students' research capability development varied the most among the institution types. Additionally, student engagement played an active mediating role in the relationship between institution type and ability development.