You could use either, or both.
The application of a Ground is related to suppressing Static Electricity for our Systems. Many, who don't wish to use a Block out on their Mast (if they have one) use a (in-house) splitter, and ground it to a near metal cold water pipe, like when the splitter is in the attic.
Many of the various TV's, Amps and DVR's have a third wire Ground included in the Power Cord. That usually is quite sufficient to suppress any accumulated charge on that, and any other equipment connected to it, by a Coaxial Cable, making supplemental grounding superfluous. However, if all your equipment have two wire power cords, then, I would recommend grounding by either application.
One should not make any assumption that the application of this type of grounding, has any real protection when considering a Lightning Strike, either locally or at some distance. That should be addressed by Suppression Technology.