Pros
Amex is a company filled with generally bright and dynamic idnviduals. The company places a strong emphasis on people leadership and development, leading bright motivated people to stay and do well, but also generating a strong "insider/outsider" dynamic where it quickly becomes clear that there is a chosen set of individuals who are being tracked for future opportunities. The firm is highly relationship driven, and building internal "champions" and a strong network of relationships is key to ensuring that one ends up on the fast track.
Cons
Comp is definitely below industry standards, but given the tremendous opportunity for work/life balance, AXP can afford to pay less since the roles are generally in strong demand in the market. The company's highly matrixed and consensus driven culture allows people at all levels to be involved in discussions on a wide array of topics (particularly nice for development of problem solving/business judgment as a junior person), but often leads to slow decision making that results in the firm missing major market opportunities.