"Espresso" and "drip" aren't types of coffee; they are types of coffee preparation: grind and brew. Drip gets a bad reputation because it's associated with offices, waiting rooms and cheap diners. The espresso method does extract a different profile of substances from the coffee; but it's subjective whether that is better or worse.

Espresso made with poor quality coffee (bad roast, crappy beans, roasted too long ago, incorrect grind, etc) is going to be just as gross as diner drip.

Another thing to consider is: you can make drip manually, whereby you control the drip rate, total quantity, and water temperature. Not all drip is automatic.