I don't fully understand the difference, however based on the current use case in discussion with the HydroShare team, as well as information found in the first link I sent you, the image pyramid is more efficient when dealing with multiple large TIF files. On HydroShare, if a user creates a RasterResource with multiple large TIF files that are all intended to be rendered as one single TIF, HydroShare handles this with a VRT file. Well, GeoServer does not support VRT files, and it seems to us that image pyramiding is the next best option. We already tested GeoServer's "image mosaic" option, but that did not work as well either.
I hope that makes sense. If you want some more detail, I can forward you some of the email discussions I've been having with the HydroShare team about this issue. Let me know.