Historically, UBA was very prestigious; but for political reasons has had a steep and steady decline (plummet?) since the 70s — very comparable to CUNY’s (the City University of New York) world class reputation in the 40s, 50s and 60s then steep decline from the 70s to now. Although my argument is correct, it is controversial with Peronists insisting that it is still the greatest university on the planet, while those who claim this but are rich send their kids to university in the USA, or to....
As of today, the two Argie universities that compete on the world stage, at the international level, are San Andres and DiTella. DiTella for example is known for its world class Econ department and law school, for example. They are also by far the richest universities in the country.
Other universities are good but glide off of their reputations from when they were better, like Favaloro and the UBA’s Med School.
The med school at the UBA is also an interesting case because: while not as great as it was, it is still fairly good. Combined with he fact that it is is free, you get fairly good students from around the world attending or as well.
Note also that the university of Córdoba is considered high quality domestically although it has little international standing.