^^ @Planner, with all due respect, I think comparing the AB Duke scholarship is apples vs. oranges. Duke is a top 10 school and is the equal of Stanford in most respects (not quite as prestigious, and not quite as strong in STEM, with some exceptions like BME); but the “dropoff” between Stanford and Duke is negligible, and the AB scholarship also provides additional perks and intangibles.
I think these kind of decisions have to be handled individually. The calculus generally would involve (1) how much of a financial strain is involved, (2) how much of a difference between the two schools there is to the applicant, and (3) the applicant’s long term plans. In the case of someone 95% sure about medical school, 4 years of medical school cost down the road plus the relative merits of being pre-med at Stanford vs. pre-med at Emory as a Woodruff Scholar would seem to strongly favor Emory; but if the OP’s daughter really has her heart set on Stanford and is going to be second-guessing herself for 4 years, that may be a deciding factor.