If academia/PhD is a real interest as OP noted, Columbia will be more prestigious, and academia does factor prestige of pedigree from what I am told by friends on the field. As an employer in the finance industry, I would also be more impressed with a strong Columbia transcript than with a strong Notre Dame transcript, personally speaking. If OP only cares about career prospects as noted, I would only pick ND if I thought that the quality of life there would drive me to a better transcript outcome, as at that point the scales would be even or tip in favor of ND.
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