Looking at DPS and Base Damage (influences auto-attack, does more damage to end-game fights than you think ^_~), the Ifrit's Harpoon is bested by the Sergeant Spear if you have the Atk Power Sanction, and the Lieutenant's Spears are above those, *assuming* you have the 5-piece bonus or the Flame Spear which has the attack power pre-bonus.

Factoring in Auto-attack and jump damage:

Lieutenant's Spear > Garuda > Sergeant/Ifrit

Sergeant offered up a 21.75% increase in WS damage, but add auto-attack and jump into that equation, and Ifrit's is 22% more damage output. I was too lazy to get exactly 7.8%, but I feel 7.1 is close enough for me xD.

My Studies