I do not think your arguement in the first sentence is valid at all. Since you used the word "majority", then basically you are saying those four schools are "far better" than five IVY schools not named HYP. MIT and Standford may worth some discussion but the difference will be marginal if they are better than the mid-Ivies such as columbia and Penn. And how can Chicago or Caltech be "far better" than Columbia and Penn? What is the basis leading to your conclusion? selectivity? ranking? or top-ranked professional school?
I would pick Duke over Chicago and Caltech. Caltech is pretty much a tech school if you ask me; it draws a small and very specific pool of applicants, and its acceptance rate is not amazingly low given its size.