Is one method better than the other? How so?
In the possible event that one has both options at their disposal, which one should they choose?
An example where you would have both options at your disposal would be wiring a ceiling light fixture, where your feeder cable contains a ground wire, and there is also a ground clip on the fixture itself. You then have the choice of attaching the next light fixture's ground wire directly to the ground clip on the previous fixture, or you can pigtail off of the previous fixture's ground wire.
When I write ground wire, I am referring to the bare or green-insulated wire.