The primary difference is that a shock hand is designed to push the energy through a contained area and outwards, while the full-body discharge transmits that juice all along your entire body as a conductor. That means that you're taking as much hit as the target, but the "pass it on" style of the Orthoskin lowers your own electrical resistance, meaning that less stays with you as it moves on down the line.
Incidently, if you've never seen how much of an Electric Eel's body is dedicated to that zapper organ, you should check it out. It's crazy. Like, 80% of its volume I think. It's like a car battery with a head stuck onto it.