I wish I had your problem of choosing between Caltech and Berkeley
I'd add LLNL and NASA Ames Research as major research institutes that are close to Berkeley.
Do you have the opportunity to come to the U.S. and visit these two schools and the places they are located at?
The strength and diversity of programs at Berkeley gives you more options in your field of Applied Mathematics, specially for someone who has yet to choose his field of studies within the Applied Mathematics.
Before making any decision, do yourself and your wife, a favor and visit these two schools.