Breaking RSA changes the world by breaking crypto and implicitly by moving protocols to post-quantum crypto, which is already happening https://security.apple.com/blog/imessage-pq3/.

Quantum computers also change the world by solving circuit-SAT https://en.wikipedia.org/wiki/Circuit_satisfiability_problem more efficiently than classical computers than.

They also change the world by simulating quantum systems efficiently, which classical computers cannot do. This has profound implications for physics.