Pros
There are many opportunities to gain a broad range of experiences in the Finance organization at American Express. In general, moving into different Finance roles is possible if you put in the time to network and build relationships. From the point of view of someone starting a career in Finance, this opportunity for movement is very attractive.
Cons
It's been painfully repeated on many other posts, but I'll say one more time that the salary is not comparable to other financial firms. You get a good work-life balance in most (not all) areas of the company, but the pay is simply not competitive. I know more than a few people who plan on jumping ship for the bigger paydays once they've gained some experience and--hopefully--a few promotions.