I'd like to quote a passage from Joseph Pieper's book Scholasticism: Personalities and Problems of Medieval Philosophy. There's a lot in the book I would take issue with, but this seems correct:
[A] word must be said here concerning the experiment with the "Great Books" which has been undertaken at American centers of learning. Here is a curriculum based on certain books which represent the cultural "heritage": their authors are Homer, Plato, Aristotle, Virgil, Plotinus, Augustine, St. Thomas, Dante, Shakespeare, Kant, Hegel, Goethe, Darwin, Dostoevsky, and Sigmund Freud. It is possible to quarrel with this or that aspect of the project. Nevertheless this attempt, carried out with the earnestness of great open-mindedness, sprang from a conviction that the young continent could come into possession of its rightful intellectual inheritance only if that inheritance were made teachable and learnable in this fashion. This is not so very different from the impulse which produced the schoolmasterly enterprise of medieval scholasticism. And not only the problems but the "problematic," which is to say the dubious, aspects of the matter are largely identical. Thus, there is the question of translation (in the broadest sense) - unavoidable under the circumstances, but nevertheless posing its own special difficulties. There is the question of the selection of the material, and the inevitable omissions. There is the question of how much simplification is legitimate, and where it is going too far. The possibly too facile determination to take the questionable aspects into the bargain, in the face of the simple vital necessity, likewise seems much the same. . . . Through such a program those American students . . . do, after all, become acquainted more or less at first hand, though in translation, with both the Nichomachean Ethics and the Meditations of Marcus Aurelius, with large parts of St. Thomas' Summa theologica and with Pascal's Pensees. And when one comes in contact with these students, one is aware of a perceptible difference. Returning to our European universities, one feels clearly that such "scholasticism" would profit us as well. It offers one of the very few possibilities of keeping at all recognizable and present to the minds of the young the "fund of wisdom" on which man lives spiritually. That fund, that heritage, or whatever we may choose to call it, has grown so huge - by a natural process, not at all because it has been wantonly accumulated - that its entirety can no longer be commanded by anyone.
Pieper makes a lot of good points here, and the comparison with the medieval university curriculum, both in its great advantages and its significant defects, is noteworthy and instructive, and I don't think I've seen it made anywhere else.
One final thing to say is that not all Great Books programs are alike. The linked article is critiquing a particular approach to the subject from a particular philosophical and political perspective. But the differences in outlook and approach between the Great Books programs of (for instance) my own alma mater St John's College and Thomas Aquinas College are enormous and very distinctive. People familiar with the two can spot a Johnnie or a Thomas Aquinas alum right away. They do tend to breed particular mental habits. Depending on the program, these can be good or bad, but are usually mixed in different ways. But I would pick any Great Books program over nearly any other undergraduate university curriculum I know for pure educative value.