Karen Tan finished her master's degree in mathematics at the University of Cambridge three years ago and set her sights on a career in U.K. finance.

But after six frustrating months failing to find a job in London, the Chinese native changed tack and returned to Asia. She eventually landed a position as a macro strategy analyst at a Chinese investment bank in Hong Kong — and she's happy to remain in the city.

As global investment banks cut thousands of analyst jobs over the past years, Chinese firms went the other way and bulked up their research departments. The divide is being exacerbated by the adoption in January of the European Union's revised Markets in Financial Instruments Directive, which will upend the way banks long charged clients for research. Chinese investment banks, by and large, are insulated from the new rules, known commonly as MiFID II.