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I hope this is a joke post, but just in case: In the real world there is absolutely no difference between a 3.70 Harvard Applied Math grad and a 3.80 Harvard Stats grad.
It depends on what you, er... I mean your "younger brother" wants to pursue after graduating. If it's investment banking (corporate finance, M&A), either major will be great. Your "younger brother" will have no problem getting interviews through OCR. Also, most people interviewing him will be former Ivy League econ majors who have probably forgotten how to solve integrals - so they will look at "applied math" or "statistics" and think, "Ok, this kid is smart, lets look at the other factors."
Now, if your "younger brother" wants to go into any kind of quant role (quant fund, high frequency/algorithmic trading, that is where things change a little. I knew someone who studied Applied Math, and when he went into an interview with a top quant fund one of the first questions the PhD interviewer asked him was "So, applied math, huh? Why not pure math?"
The most important question is: what final club / frat / eating club is he in?
don't major in statistics. A lot of schools don't even offer it as an undergrad degree for a reason. A real mathematician will not be impressed because real statistics theory relies on knowledge of analysis/measure and you must have a grounding in pure math before you can handle it.
Most people will be much more impressed with a 3.5+ applied math major than a 3.9 stats.
Only math nerds, not organizations looking to hire people.
Except many people on wall street now (especially where a mathematician would be getting interviewed.....) are "math nerds", so there's that. Don't lump the majority of society into your inbred world, thanks.
Majoring in applied math does not make one a "mathemetician." He's not applying for a gig with DE Shaw or RenTech here, numbnuts.
For business school, consulting, and banking (the three things OP mentioned), a 3.9 in stats is far better than a 3.5 in applied math.
If you're looking for a quant role they'll care about your gpa and what programming languages you know. If you're applying anywhere else it doesn't matter.
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