For graduate school, is Cornell or Yale generally considered the better choice?

The biggest practical tradeoff is breadth versus brand shorthand: Cornell has enormous graduate depth across many fields, while Yale often carries a slightly more instantly recognizable prestige halo in the public imagination. Cornell is especially formidable in engineering, agriculture, architecture, hotel administration, labor relations, and several applied sciences. Yale, by contrast, is smaller and more concentrated, with exceptional visibility in law, medicine, public policy, the humanities, and many social science areas.

In academia and among serious employers, the specific department usually matters more than the university name alone. A PhD from a top-ranked Cornell program can be viewed more strongly than a Yale degree in a field where Yale is less central, and the reverse is also true. Faculty reputation, research output, advising, funding, and placement record tend to carry more weight than the broad question of which school is more prestigious overall.

If you mean overall reputation in a non-specialist sense, Yale probably has the edge in pure name cachet. If you mean graduate education as an ecosystem, Cornell is often underestimated because it has so many high-level programs and a very strong research footprint across disciplines. People inside academia usually know that Cornell is not just "excellent for an Ivy," but a major research institution with elite departments in numerous areas.

So there is no real blanket answer that Yale is better for graduate school. Yale has the more universally glamorous name, but Cornell is just as strong or stronger in a substantial number of graduate fields. For graduate school, the smarter comparison is almost always Cornell department X versus Yale department X, not Cornell versus Yale in the abstract.