My take is that it is very hard to make the transition from research to PE, although it's not to be ruled out. I know it's possible because i've done it myself. As far as PE is concerned, they definitely care a lot about pedigree, i.e. you need to demonstrate that you did well with in research, great undergrad degree and other interesting extracurriculars. Make sure that you have a good story as to why you want to do private equity, and of course, know how to build LBO models inside-out and be prepared for private equity case studies. Finally, fit is also very important in private equity, so you really should have a very strong idea of why you want to do PE and that you have the type of personality that would succeed in PE.
Most times people leave research and go into asset management or hedge funds because that's really the natural transition, but keep in mind that to get into the hedge fund industry is far from a given. You will have to be competitive, know your coverage space very well and demonstrate that you know how to think like an investor. All in all, you will always need to be able to prove your case a to why they'd rather have you instead of one of the very many investment banker.