If you'll notice, most of the abilities you get with the shield are those that improve drops, increase munny and HP/MP balls and whatnot.

Strength gives you the abilities that increase your physical attacks. Air combo +1, combo +1, vortex, etc.

Magic gives you abilities like MP Rage and increase your MP.

As far as the shield job giving you a naturally better drop rate, I've got no idea.

EDIT: Behemoths can be fought over and over again by going through the exit of the first area of End of the World.