For reference and clarification for anyone reading this, @IldarW is referencing your backup codes/seeds for each of the sites that you use Authenticator for, not the backup code for Authenticator itself. Google doesn't offer a backup/restore for your Authenticator account. While some people view this as a security feature, I view it as a nuisance. If you lose your device, or if your device crashes, you are out of luck when it comes to restoring the sites that you use Authenticator for.
There are still a good percentage of sites who offer 2FA who do NOT give you an option to backup your seed. This means that you would have to fully rely on Google Authenticator, and that you trust yourself not to lose your device, trust others to not steal your device. If you ever lose access to your Google Authenticator, you are shit out of luck with any of the sites that require 2FA logins where you didn't backup your private seeds/keys.
I'd also like to inform you guys of an incident that happened to me recently: I upgraded my phone, and backed up my old device. I restored the data to my new phone. I thought the settings for Authenticator would port over, and that's when I realized that there is no way to transfer your 2FA to YOUR OWN new device from your own former device.
Yes, Authy is less secure than GA, but much more convenient. And as long as you keep your master password different than any other password you use, and follow strict recommendations of what types of passwords to use to create your master account, you'll be fine. And you're free to authorize other devices to use your account, as well as able to easily backup and restore all of your private seeds.