While drip coffee can be quite good, I'll take the taste of a properly done espresso over drip coffee any day.
I'll agree with bensyd: I found the flat whites I tasted there to be superior to anything similar you can get at an American coffee house (a latte at the better of my local places, such as Kaladi Brothers or Cafe Del Mundo up here in ANC). Espresso culture seems to have been around in Australia longer and had more time to embed itself in local culture and develop proper technique than it has in the U.S., where it's come around mostly since the Starbucks revolution.
I also love the French/Spanish/Portuguese/Italian strong coffees (Café au lait, café con leche, café com leite, caffè latte) and have yet to find something similar in the States (a latte at a modern coffee shop isn't the same thing). In fact, can anyone tell me what process they use to make those? Is it indeed espresso, or is it a strong drip or French press coffee? If it's espresso, why don't lattes at coffee houses taste the same?
There is one large benefit American drip coffee has over espresso: it's cheap. Even at a good coffee shop (like Kaladi's up here), a 20-oz drip coffee is $2, compared to $4-5 for similarly-sized espresso beverages. And that's for good coffee; if you don't mind drinking swill or watery cardboard, you can get unlimited refills at a neighborhood diner for under a buck (still, I think; I haven't checked recently).