Assuming sell-side...
When I was in risk management working for a top tier bank I was interested in Equity Research and spoke to over 20 members of the team. Eventually I had to take two internal tests to qualify for the role. I also interviewed extensively at another large bank and had a similar experience.
Education: MFE is not the right fit for ER. Most managers I spoke with were not even familiar with the MFE degree. There will be virtually 0 overlap in skillset.
Required Skills:
1) Soft-skills - You will be on the phone with hedge funds all day. You will be emailing your own feedback/analysis/presentations to clients.
2) Accounting - Understanding the 3 main accounting sheets and how they tie together. This was one of the two tests I had to take. It is far more advanced than accounting 101 though; so be prepared. WallStreetPrep course on this was insufficient.
3) Writing skills - This was test #2. You need to write recommendations on stocks long-hand. Also, when your predications turn out incorrect, you will need to pen explanations on why that occurred.
That is it! As you can see, virtually no overlap with MFE.
Just to close out:
Pay: On par with S&T
Hours: In between S&T and Investment Banking
All in all I think ER is an excellent career choice but the barriers to entry are very high.