1. It has a rock solid dispute system. I've disputed charges where the merchant didn't deliver on promise and AMEX took really good care of it. Same thing with a Visa card didn't go very well. You can do everything off the AMEX website and over email. With others, you have to call them and deal with lousy customer support.
2. They have a really good website and overall user experience. Its a pleasure to go to the website to see the charges, or to get a well laid out annual spending report. Their mobile app is also the best as compared to others.
3. They have stellar customer service. I rarely need to call them, but when I do, the wait times are in seconds.
4. They support mobile payments - Its the first one to be on Samsung Pay and I happen to have a Note 5.
FWIW, I just have the "American Express Blue Cashback" card, which no annual fees.