Storing 2FA codes is just the beginning. Bitwarden aims to add defense in depth to authentication.
Bitwarden Authenticator is a standalone app that is available for everyone, even non-Bitwarden customers.
In its current release, Bitwarden Authenticator generates time-based one-time passwords (TOTP) for users who want to add an extra layer of 2FA security to their logins.
There is a comprehensive roadmap planned with additional functionality.
Switching would probably be a mistake because storing both your passwords and 2FA info in the same password manager is not a good idea, since if your password manager account gets compromised 2FA will do nothing. You should use a seperate 2FA app, and Aegis is a pretty good one.
Is there anything about Aegis that makes it better than Authy? Just looking at the page for Aegis, I'm not seeing a lot of difference. And it being Android only limits it.