Pros
The number one pro is the people you will work with: Amex attracts people who are not only smart and driven to succeed, but in general are willing to help others along the way. It is a highly collaborative environment - in part this is forced by the matrixed organizational structure, and this can be a negative in that it slows down decision-making, but it is also an outcome of the type of individuals who get hired, and who stick around. Second, while it is a brand-driven company renowned for its advertising, it is a fundamentally sound business with extraordinary attention paid to risk assessment and quantifiable outcomes. If you don't have a finance background or an aptitude for numbers you can certainly get by, but if you can combine quant savvy with creative thinking and influencing skills you will do very well. Management is generally very open to work-life balance needs, and takes employee development and satisfaction extremely seriously. There are exceptions of course, but there are a lot of good people leaders here.
Cons
Performance doesn't always guarantee career success - beyond a certain level - probably Director or above - you need a senior leader acting as your 'champion', to get you in the door and then keep you moving forward. The company tends to dip its toes in cutting edge segments, but when times get tough they are the first to go regardless of their strategic, long-term importance. The need to manage multiple stakeholders for every decision can be frustrating, and often there is no clear 'owner' for a decision.