Everyone has already mentioned the biometrics, but I think even without that you still should have to suck it up if you want to improve your security.
Also, I think it's worth the hassle of changing to Aegis since you can make backups of your vault pretty easily, something which Google authenticator doesn't provide.
The only option in that app is cloud sync which IIRC isn't encrypted in any way, so your keys are being sent to you-don't-no-where via you-don't-know-how in plain text.
Aegis gives you the option to sync your vault with an encrypted file which you can then import into other Aegis install (I don't know if it has the option to sync an unencrypted version).