You seem to be looking for ways to justify going to Brown. Discuss it with your parents it is their money, not ours.
I do not think you would be disadvantaged coming from Vandy or Brown. If you are concerned speak to both recruiting offices and see what they say in terms of employment statistics. Undergrad business is a fairly new concept for most top tier schools. Most wall street firms these days seem to want quants. So as a math major with perhaps an econ minor you would be fine coming from either school.
With all due respect, neither school is a HYPSM. Before anyone attacks I know there are many schools that will better prepare you, will be a better fit and so forth, what I mean is if you want that name recognition, that perceived entry into Wall Street, the two schools are fairly equal.
While I would have loved the idea of Brown for my older kid (was not accepted), because there are a number of small advantages that will bolster GPA, like the long add/drop period, which when you inevitably take that class that you either lose interest in or is too hard for a Freshman and you can still get out of dodge without ruining your GPA. I do not know that much about either school but that is something I like about Brown however, my kid is not going there and kid will manage where kid is going and that small thing is not worth $135k to me. However, if there are other small advantages to Brown, you and your parents need to explore them.
Learn absolutely everything you can about both schools, understand their rules, ask questions on their forums, visit again this week if you have to. Then make a decision with your parents.