So I've been doing my daedric artifact quests, and I have two different ones now, but I'm a bit confused as to which is actually better.

Dawnbreaker, the sword, does 18 points of base damage and 12 points of fire damage on hit

The Mace of Molag Bol does 24 points of base damage, as well as 30 points of magicka damage and 30 points of stamina damage per hit.

It would seem then, that Dawnbreaker is better than the Mace, because 18 + 12 = 30 damage per hit (though I'm not entirely sure how much resistances end up cutting down that 12 damage) but the game gives me the little upgrade triangle on the mace when I have dawnbreaker equipped. What am I missing here when evaluating which weapon is better?

For health damage, the dawnbreaker is better for you. For damage overall to health, stamina and magicka the mace does more.

Dawnbreaker does more damage against armored enemies that are not resistant to fire (fire enchantment ignores armor rating), and it is capable of hitting with crits. Mace of Molag Bal does Stamina and Magicka damage however, and with perks it ignores a large portion of armor defense.

I would recommend Dawnbreaker against undead and MoMB against bandits and mages.