The short version
The Hypervolt 3 Pro leads on power, quiet and price; the Theragun Elite leads on stroke depth (16 mm) and the Therabody ecosystem.
When the Hypervolt 3 Pro is the right pick
You want the strongest, quietest, longest-running gun for less, and don’t need Theragun’s deeper stroke.
When the Theragun Elite is the right pick
You want the deeper 16 mm amplitude, the Therabody app and multi-grip handle, and the ecosystem matters.
Also worth comparing
For Therabody’s flagship, see Hypervolt 3 Pro vs Theragun PRO Plus. Full field: best massage guns.