For a Math PHD, Rice will make a difference.
For a PHD in Economics, for both, look at the choices and math content at the upper level, email each department to ask what upper level courses are on the annual rotation, what as offered this year, what Econ graduates did (PHD programs or jobs).
Someone who majors in Math or Applied Math or Statistics and/or Economics would have no problem finding a job provided they use the career center and their adviser.
You can try to differentiate in terms of professional outcome.
You could also look at total experience (ie., residential system, etc) to weigh whether Rice would “fit” him better.
Keeping in mind USC Honors is one of the top Honors Colleges in the nation, has a nice campus, good weather…
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