Quick answer. Push notifications require the customer to have installed your app and opted in; RCS reaches the native inbox with no app at all. Push is effectively free per message and great for re-engaging existing app users, but its reach is capped by app installs and notification opt-in rates, and messages are easy to dismiss. RCS reaches a far larger audience (anyone with an RCS-capable phone), carries richer interactive content, and persists in the inbox — at a per-message cost.
Use push to re-engage your installed base at no marginal cost; use RCS to reach the much larger group who will never install your app but will read a branded text. For many brands, RCS is the way to get app-like engagement without app fatigue.