I have some first hand experience in this sort of thing. :-) :-)
Harvard, Princeton, and Yale cosmology Ph.D.'s tend not to get hired by Wall Street firms because they can usually find a job in a national lab or academic post. The astrophysics Ph.D.'s that tend to get hired in finance are Ph.D.'s from other schools, because they are locked out of the academic job market.
You'll probably reach the wrong people. One problem with getting a physics Ph.D. job in finance is that if you talk to someone in HR or someone that does general recruitment, they are usually pretty clueless. Also the firms that hire physics Ph.D.'s are the firms that you've heard in the news. Morgan-Stanley, Goldman-Sachs, JPMorgan, Deutsche Bank, UBS, Credit Suisse, and those are just the investment banks. There are also hedge funds (Blackrock, DBShaw, RenTech, and probably fifty others that I haven't mentioned.)
There aren't a huge number of jobs, but there aren't a large number of applicants. In a good year, a bank may hire about a dozen or so physics Ph.D.'s, and your typical investment banks will have about 100 or so STEM Ph.D.'s in a head count of 30,000. But a 100 Ph.D.'s is a lot of hiring.
Do what you love. If your primary consideration is career, the MBA will be better. If you are totally committed to learning physics, then go with the Ph.D.