Elemental Damage Question

So my warrior has two swords.

#1 Damage 13-19
#2 Fire Damage 14-21

My experience so far is that sword #1 almost always seems to do more damage. Why is this? I would expect elemental damage to typically be more robust and 'armor piercing' against enemies.

Are Strength and Swordsmanship less effective with elemental swords? Or is high physical armor actually less common than high elemental armor? Or am I just imagining things?

do you meet the requirements on those weapons?
are they both customized?
do they have any other mods that may increase damage?

Yes to questions one and two.

They both have damage boost abilities, but I checked for that in my 'sample'. (One is while health is below 50, the other is while enchanted.)

Sword number one has Armor Piercing +10% (8% of the time)... this doesnt seem like it would affect things too terribly much, however.