I was just researching this like an hour ago. I want an Amex, and I hear they have decent benefits/rewards/protection. One compliment I hear about them is their service. Apparently it's all US-based and good quality, which is good if you've ever had to deal with some Indian on the phone for half an hour. I think for my spending habits though, my Discover card does me just fine (just a lower acceptance rate). It'll probably be at least a year before I apply for an American Express.
@SilvioDante If you're talking about Amex being charge cards (the kind that require payment in full each month), it is worth noting that not all of them are. The Delta one that OP mentions happen to be a traditional credit card.