Vantaggi
Relative to its peers, especially in NYC, Amex work culture is less intense while still challenging and, in most cases, rewarding. Some of the smartest and most talented individuals work here. There is a strong focus on ethics and compliance, but at its core, the company truly does look after its customers' best interest (which cannot be said of other banks), and this of course is exemplified by its much-vaunted customer service, as any cardmember can attest to.
Svantaggi
Innovation can be slow sometimes, although for an ancient company, it's doing a decent job at staying relevant. As a whole, it is risk-averse and more of a fast follower than an early adopter, so to speak. Compensation is at par with, or only slightly better than, industry average, which means that in super-competitive NYC, yes, you will get paid more working for a competitor (although one has to keep the work/balance thing in mind).