I actually looked into Drilbur about a week ago.
When you first get it, it's level 13 at MAXIMUM, which by that stage it barely has a single good move and is a good bit away from getting Dig, that combined with N's Second battle having a really strong Tympole packing Bubblebeam does just over half of Tepigs heath, never mind Drilbur being a lower level at the time so it would do MORE to Drilbur. The fight is likely even more inconsistent than it is with Tepig.
Plus I have absolutely 0 ideas how you would beat Burgh with Drilbur.
If anyone else has more insight it would be helpful, but that's what I gather. Tepig would by far be faster than Drilbur/Excadrill
Also I don’t think that Exca gets iron head in this game. It’s taught by move tutor in BW2