This paper compares university competition through fees (as in Anglo-Saxon countries, following Bertrand competition) and admission (as in old European countries, following Cournot competition) in a setting where universities endogenously choose their capacity constraint. The results show that, with competition over fees and sufficiently convex costs, universities adopt a low capacity to set higher fees. This capacity adopted is efficient in terms of cost minimization. Then, we find that introducing a new university is welfare improving in Bertrand competition. Conversely, competition over admission leads to a higher capacity and a greater number of students enrolled per university, which may be detrimental to welfare.