Pros
The Whitehead is a fantastic scientific institute where the most cutting edge biology is taking place. They invest many different programs to take care of their postdoctoral fellows (computer programming courses, grant writing). WI is at the forefront of pioneering efforts to bring great benefits to its hardworking postdocs. Its a great collaborative environment to get science done across multiple disciplines. The Broad Institute and HMS are very close...it never hurts to be around lots of smart people who can help you get things done.
Cons
The major downside is the high level of competitiveness at the Whitehead. You have to realize that you are dealing with some of the most competitive investigators in the world. You have to play their game and learn their rules. Protect your ideas and your work because you never know who will take them from you and claim them as their own...