Hi youknowhoo,
I thought I’d take a stab at answering your questions, although I’ll caveat that I have not been involved with the subject for a while (since ~2012 when I myself was looking into pursuing a graduate degree), so I’m sure others may have more updated views. I'm also not sure how much detail you're looking for, so here's a pretty long post.
MFE and MSF are obviously both finance degrees but the approach each takes is vastly different. Also, they each target different prospective students so think about what suits you better. In a nutshell, MSF will have a strong focus on corporate finance and financial management (three statement analysis, ratios, accounting to some degree), while MFE will mainly deal with the more complex mathematical theory that aims to understand how public markets operate (probability, statistics, pricing theory).
MSF programs are tailored to people who don’t have a finance background (and likely not a quant background either) and are looking to land a corporate job. Most of the MSF programs I’ve seen are pretty equivalent to an undergrad degree in finance (both in content and difficulty), although some have flexible curriculums that will allow you to tailor your education. Think of these programs to be well-suited for someone who majored in say, marketing and is looking to break into finance. I've also seen a lot of industrial engineers that go for MSF programs.
As for MFE, in my experience, it will not turn you into a rigorous quant, but rather teach you enough math to understand what real quants are talking about and working on – so the ideal role for a typical MFE grad would be to provide a link between management and the quant teams that develop a lot of the tools in a bank or a trading shop (which is why Risk Management is a good fit). Also, MFE programs don’t seem to be very standardized (at least they weren’t back in 2012), so some have a greater focus on math, while others tend to teach more traditional finance or computer science or any mix of the three.
In terms of career opps, candidly speaking, the school you go to will be the most crucial factor. An MSF from the University of Utah won’t get as many recruiting / interview calls than an MSF from Princeton or MIT. That said, the scope is broader for MSF than for MFE – you could land a job in both the financial industry (banks, HF, PE, VC), and outside of it (corporate roles in any company in any industry). MFE career opps will be usually limited to certain roles within the financial industry.
Can you get a non-quant role after an MFE? Yes! That's actually what I ended up doing, although I majored in finance as an undergrad, so I was never an actual quant.
Now, not part of your two questions but you mentioned your priority is to work for either a PE shop or a Hedge Fund. I’d note that these roles would be very different from one another and will require pretty different skillsets. Both are incredibly competitive so my point on selecting a target school is even more critical (I’ve actually seen HF recruiters take people’s resumes and immediately give them back to the candidate because it does not say “Harvard”).
- PE shops recruit their juniors exclusively from Investment Banks (at least MM and mega funds do), so you’d need to recruit for IB beforehand and learn as much as you can about M&A, LevFin and ECM. In fact, that’s a very usual career path for IB analysts. PE shops tend to hire from a few IB groups but will focus on the M&A and LF teams. Also, note that if you’re already at the graduate degree level, you’d come into IB as an Associate, not as an Analyst and PE firms are less likely to hire Associates than Analysts – just something to consider
- HFs deal directly with the public markets, so a lot of the operations have become quant-oriented. However, more fundamentalist shops still do a lot of research that deals with “traditional” finance (going through filings, press releases, dialing into investor calls, etc), but also have to prove that you can think outside the box to conduct research and find good investment opportunities. For instance, I heard the story about a HF that used to take weekly pictures of a retailer’s parking lots across a bunch of different store locations to determine how sales were going to pan out the next quarter. Or there’s the urban legend of a HF manager who used to buy one muffin from a coffee shop chain every day to see the ticket number and get a sense of how many tickets (sales) they were issuing. I’ve seen HFs hire from Industry Coverage IB groups because of their industry-specific expertise. I defer to others to opine on how likely it’d be to get a decent HF job straight from graduate school, but they will obviously prefer someone with actual experience and proven motivation / desire / capacity to prioritize their job above everything else
