Pros
I worked in AMEX for four years right after my PHD studies. My first year experience was good, second year was ok, in my third year I was trying to get out and in the fourth year I couldn't take it anymore and was ready to accept any job offer outside the company. The pros is you can learn some basics about cards business and there are lots of young people, so if you are a young person you would like it. There are lots of employee activities and you can participate in any of them provided that you complete your work on time. There is also an Asian Employee network.
Cons
The culture there requires you to find a place to transfer internally after a couple of years. If you cannot find a place then you would be stuck there for a while and do things that create no value for your career and the company. The management looks democratic but actually similar to dictatorship. There is too much politics going on there and there are many very talented, knowledgeable people who have never been promoted because of all these politics. Do not expect to climb the ladder in AMEX unless you are a minority or know someone in high position. The pay is very low for New York City standards but since most people commute from NJ this is not a big issue. You work with internal business partners and their bad opinion about you counts but good opinions are ignored most of the time. If you have low rating because your boss thinks that way, you are given some time to correct your performance but I never witnessed anyone who went through the process and able to keep his job. In other words if they don't like you for any reason -non work related, they find a way to send you away.