Pros
You will get to take on projects and responsibilities that essentially nobody else gets to take without any experience. In the 4 months I've worked with EA, I've run 5 press conferences, been published in almost a dozen newspapers, lobbied a U.S. Senator, 1 U.S. Representative, and 3 other Representatives' staffs, and over a dozen State Representatives' and Senators' staffs.
Cons
Terrible pay - it's the minimum for white collar (with the exception of in NY and CA, where the salary is higher), which is lower than the hourly minimum wage by 30-40 dollars per week over the course of the year; that's thousands of dollars per year. Hit or miss "staff director" model - Fellows are paired with experienced Advocates and members of the Field Team, and while I know many who are very happy with their director, many are unsatisfied with theirs. Extremely long hours - at the minimum, expect to work more than 50 hours a week, and during the summer, you'll be working at least 65-70 per week.