There are many advantages: Lighter finger grip needed in either orientation which smooths release, lowers fatigue and adds stability. Arms and elbows tucked tight to the body for higher stability, adds a stop in lower speed for acceptable camera shake. Allows critical adjustments easily while your eye is at the VF since both command wheels, AF-On, and multi-selector are in normal positions in either orientations. Reduces perceived weight of the rig and lowers muscle fatigue in both orientations. The most important reason is that it just feels better in the hand.
The extra battery is nice but not as beneficial as the above reasons to have a grip. Some one on another from suggested his reason for having one is that "chicks dig it, think I'm a pro who will get them a modeling contract"