I asked this question a few years ago when I was applying. The response I got was something like this:
"If you have been working in industry for several years, we understand it can be very difficult to get academic letters of reference from professors who remember you... however at least one letter from a professor who can speak to your quantitative ability would be preferred."
In reality, I just went with three professional references. Two of those references were PhDs doing quantitative work at a bank, with published research, who had MFEs working for them; one was my current manager. I was admitted without any letters from professors, but I had also been working in industry for 4.5 years when I applied.
I would still check in with the staff. Melanie Heaney-Scott, Wendell Colllins, and Karen Neukirchen are all a bit more familiar with the admissions process than I am.
I have a feeling that all else being equal, if you must go with a professional reference, having a reference that meets some or all of these characteristics is more helpful:
1.)
The referrer can credibly speak to your quantitative ability.
If you're a programmer or an engineer, you're probably set on this front. If you're a CPA at a Big Four firm, and surrounded mostly by people with accounting educations and backgrounds, you need to choose your reference a little more carefully. (Not that CPAs aren't quantitative, but we are talking about your ability to do calculus and stats as part of a graduate course of study.)
2.) The referrer is your current manager.
3.) The referrer has a STEM, Finance, or Econ PhD
4.) The referrer has published research.
5.) The referrer sits in a role at a financial institution that involves quantitative financial analysis and requires a quantitative PhD or Master's degree (there is some overlap with 3)
But please speak to Karen, Wendell, or Melanie and let us know what you hear from them.
http://www.princeton.edu/bcf/about/contact/
Phone: (609) 258-0770
Best of luck with your application!