It really depends. If you're making them come to you, and you're suffering something like a 3 on 1 attack plus bombardment, then yes, Drill can be vital for defense since you will need both the Drill bonuses and the terrain bonuses. The unit might not survive attack, even then.
When you're the one attacking, then it's a different story. Drill lets you attack entrenched units better, while Shock allows you to survive attacking units in open terrain, which is the best time to attack them.
Or you can use Horsemen and then retreat them behind Drill units. That works, too.
Oh, come on now. The computer is terrible at using terrain defensively. Simply dont attack entrenched positions, unless they are archers/siege engine, in which case you can usually wipe them out with minimal damage regardless.