If you were going to chose between the two, then always choose Drill Run.
Drill Run has the same power as Dig, but only takes one turn to do it. It also has a high critacal hit ratio, so you can get luck easier! :)
Don't worry about the 95 accuracy, it will almost never miss.
As Dig takes two turns, its power is essentially halved to a measly 40. When underground, you can still actually get hit by an Earthquake, and not only that, the Earthquake will hit with double power!
In competitive use, Dig is pointless, because if you use it your opponent will instantly switch into a flying type, and the Dig will do nothing. They will then also have the advantage.
However, Earthquake is better than both of them so why not use that? :)