I've double checked the result from both ffxivapp and LogRep and am quite certain that Sword Oath damage is either counted in the auto-attack damage or aren't listed at all. I'll have to contact the Paladin for his stats (he was using a Lalafel in full Darklight and Vit accessory with a ring from Amdapor Keep if I remember correctly) but I can provide my own as I recorded one of my session along with my gear and stats sheet. As for the difference in damage done, the only reason I could have guessed was that he ran out of TP significantly faster than I did as my test usually last slightly longer than 3 minutes while his on average were around 2 minute 30 seconds. I do have a parse from LogRep that ran for 2:34 and was in similar range with the PLD's damage so that might come in handy as well.

Video link to rotation and stats
Warrior Parse in 2:34 in LogRep