The student can realize his full potentials in either school, regardless of major.
Winning the full ride scholarship at Duke automatically gives the student an head start in name recognition at least at the first year. The selection is competitive. Plus, the student also gains more bargaining power with his parents on spending money. The student has more freedom deciding what to do in his social time.
The student can do the same thing at Stanford as well, though he has to consider budget first.
Go with Duke. Take full advantage of the full ride scholarship, literally.
