Questions on Damage Types

OK, I got myself a 6-28 Axe that does PIERCING damage. Now...I heard piercing is better than slashing, but correct me if im wrong (and if there is a lot more to it, by all means explain the different between the two). Alas there is also fire, cold, earth, etc. damage upgrades. Im wondering if any of these would be better to get, or would it replace the piercing damage? Im just trying to create the best axe for myself here and money isnt much of an issue. So far I have a 6-28 piercing axe with +11% dmg while health is above 50%...now just need to add the upgrades, thanks.

Some class armour gives protection vs types of damage. i.e: Piercing.

That doesnt really help....does the same go for slashing? Which is better? In which situations....etc.