Why? Well, because they have better machines. But, in reality, there is so much more to the making of coffee than a good machine. Great coffee can be made with a French press just as well as with a $600 espresso machine; the technique just needs to be learned.
In addition to the differences in machines, the quality of coffee beans found in Europe, and roasting processes vary and really do affect the bitterness and richness of coffee flavors. Another aspect of the coffee making and drinking attitude that varies from America, especially, is the existence of the Americano. In the United States, regular coffee best approximates the European Americano, because of the existence of so much extra water. In a European café, you are most likely when asking for a coffee, to end up with a single or double espresso shot, or a latte. The coffee in both of these drinks just ends up being stronger, and so the flavors come out better. Those who often turn down milk or cream in their watered-down coffee drinks, often change their mind after tasting how wonderful and strong a latte (café au lait, café con leche, cappuccino…) can be.
At the end of the day, the European experience of drinking coffee (especially in Southern Europe) is so much more inclusive and enjoyable than in other places where coffee becomes just a means to get in some caffeine and start off the day. In Europe, coffee represents a break time, a time to slow down in the middle of the busy day, an excuse to get together with friends, and something to sip on for a long while on a terrace or by a window and watch the world go by.