Both schools are feeders for top management consulting firms. Stern has the Consulting IMI program which is great for career switchers like yourself, but I don't think I would turn down a significant scholarship if I were in your shoes. If it were equal cost or even a small scholarship for Duke, I would recommend Stern for the IMI, the location and the finance department.
Stern is often described as "not good for X" because it places a relatively small percentage in X line of business compared to other schools. Take this with a grain of salt however, because a large percentage Stern students go into finance
by choice. Does that mean they couldn't get into marketing or consulting, etc. if that were their goal? Probably not. Firms from all industries recruit on campus, and because of its large class size, Stern places a lot of graduates into a lot of industries. But a poor interpretation of the data can lead you to believe that having a premier finance program is a drawback, which obviously isn't the case- particularly for management consulting, where there is quite a bit of overlap with finance and having access to Stern's program would be a big advantage, especially if you have a non-technical background.