American Express is accepted in far more places in the U.S. than in Europe. On cruise ships, almost all hotels and most restaurants will accept American Express. Small restaurants and business may not because Amex charges a higher merchant fee.
I use Amex for most of my purchases and always use it to secure my onboard account.
American Express also has the best fraud department and fraud detection. If transactions do get through they will take them off with no questions asked. They also are better than ANY other company in getting you a new card if yours is lost or stolen. I had one within three hours when we lost ours a few years ago in Barcelona. I just went to the American Express office a few hours after reporting it and a new card was waiting.