^^ At least in Catholic circles, it seems that the Franciscan university that I most often hear about is the Franciscan University of Steubenville. From what little I know about it, it also emphasizes a traditional core curriculum. Compared to the Jesuit universities, which tend quite liberal, its reputation is as a bastion of conservative Catholicism. I don’t know to what extent this conservatism carries over to the several other Franciscan schools, (http://franciscancollegesuniversities.org/members/), though theologically Franciscans have always tended to be identified with social justice, peace, and environmental concerns.
The Jesuits also have the more intellectual reputation compared to the Franciscans, who did not place as much emphasis on their educational mission, though historically there have been some prominent Franciscan scholars and scientists.