In case you haven't read it, the wiki page Harness explains this.

Harnesses have two effects: they change the type of damage (normal, piercing, elemental, or shadow) inflicted by your battle sprite. And the higher-level harnesses also reduce the cooldown for sprite skills.

In response to your specific question: The elemental harness will be slightly better than your original harness when you are fighting undead or constructs. And it will be much worse when you are fighting beasts or gremlins. (No difference when you are fighting slimes or fiends.) If this is confusing to you, then the wiki page to read is Damage.