Greatness surely is an privilege which has besought corporeal entities from attaining ephemeral qualities, i.e. ambition, aspiration, attainment, etc. What ought to be understand by man is this: Greatness is rather subjective as the understatement of this premise supposes. 50 years to this day societies will have been understood under certain aspects which underlie this.
An educational institution can be judged objectively. The most notable and reliable way is using the quality of work produced by its students both while there and post-graduation to compare it with other schools. While institutions may be juggled in rankings, which certainly are subjective, the great ones do not move much for a reason: they attract the best students and produce the best graduates on a consistent basis.
I believe that the greatness of an educational institution is not subjective. There are many ways to objectively measure greatness. For example, an educational institution can be deemed great by successful athletic programs. Academic greatness can be measured in ways such as grades of students or success of its graduates. Even high retention and graduation rates can point to a good education institution.