Finally, a thread I can add some value to!
I was in similar shoes when I first started; long-term I thought I wanted to work on the equity side. However, after my experience on the credit side, I know I made the right choice, and my interest lies with the distressed/special situation names (which really have both a debt and equity slant). That is not where I work now, but I do a lot of work with those desks.
First, to clarify, I am talking about credit research (corporate bonds and credit default swaps). RMBS, CMBS, Credit Card ABS, et al research would still fall into the fixed income arena, although these are not directly transferable to covering either credit or equity.
Particularly within credit, high yield research is closer to equity research as you are more reliant on accurate cash flow forecasting and are more able to take advantage in the upside of the business.
Also of note should be that as a fixed income analyst you will likely sit on a trading floor. Its a much different environment from the equity business, unless you are a desk analyst. I love it, but others might hate it and prefer a quiet cubicle.
As far as prospects; I am more bearish on the future of sell side equity research, but its not exactly peachy for the credit side either. One benefit on the credit side is that we help our desk manage positions; credit is not as liquid as equities so many trades require taking on significant risk until you can unload the inventory. This necessitates people that understand the company and also presents the opportunity for greater profits (or as in this last year, greater losses).
Equity and credit have similarities and differences, but you still learn how to look at a company in either case.
Also, note that there is a difference between a counterparty credit analyst (risk management) and a credit research analyst (client facing research), so just be clear on what the position is.