From everything i've heard - majors do not generally factor in to service selection. Quant Econ and Operations Research both fall under the Math department. In the case of Quant Econ, if you look at the course schedule you will see QE is more like a Math major with a minor in Economics.
Mids have plenty of opportunities to get these kinds of details at major open houses, Q&A with profs and talking with upperclass. Depending on what group they are (1, 2, or 3) will drive what kind of math and engineering courses you take. Wires vs sparks is an example. That is Mid lingo for EE, but the classes vary depending on what group you are.
OP. Just my opinion but the main difference between Econ vs QE is the kind of career you want after the Navy. QE is more specialized - look at careers as an Actuary or a Quant on wall street. Lots of statistics and number crunching. Pays not bad either. Just depends what you want to do.