Okay, so I carried out a test, with Xatu using Faint Attack on Espeon, and then Drill peck on Espeon using the psypokes damage calculator. This is what I found:
Faint Attack: Average damage - 96.99
Drill Peck: Average damage - 119.39
I did one further test, this time on a shuckle -- so I could find out which one would be better all round:
Faint Attack: Average damage - 21.12
Drill Peck: Average damage - 33.2
Well, I have to admit it - you guys were right! You've got me persuaded!