Quantum-resistant cryptography already exists, so banks and other centralized institutions are in a much better position to recover.
With Bitcoin, we have much bigger problems. Simply switching to quantum-resistant signatures doesn't solve the issue because we can't force people to move their bitcoins to safe addresses. Something like 1/3 of the circulating supply is at risk -- quite possibly more -- due to key reuse, xpub sharing, pay-to-pubkey mining, etc. If a QC attacked Bitcoin in the wild, it would irreparably destroy faith in the currency based on that alone. I don't believe the same is true for banks.
People would be stupid not to move if the encryption was under threat and we could actually force them by requiring them to change addresses if all wallet software developers accepted this change.
Forcing people to do things goes against the Bitcoin ethos. That's the crux of the problem.
We could give people
several years to move their bitcoins to quantum-resistant addresses before destroying them. Even that seems incredibly controversial
based on these user reactions.
Forget block size -- this is the real political issue of our day.