There are several ways to fish a Ned Rig, as there are a typical shakey head, but I simply look at it as the most "finessey" version of a shakey head as possible.
The only distinction I can make between when to fish one over the other is related to cover and water clarity, perhaps. If the water is dirty, I might prefer a larger profile bait than a T.R.D for instance. And if there is a lot of cover, more specifically wood and weeds, I'd probably recommend something without an exposed hook, like the Ned Rig.
Just my two cents, hope this helps.