I usually save both. They serve different purposes, and even if they can be used in place of the other, they are best used for their own purposes.
The setup key is used when you lost your device, or you setup a new device. Just importing the key is easier than to get online with the one-time backup code, removing the 2FA, and inserting the next one. And depending on the service, there's a lockdown period when you are not allowed to perform some actions, like withdrawing crypto coins, for example.
And the one-time backup codes are good when you don't have the device, but you didn't lost it. Maybe the phone was left home, or the battery died and you got no charging cable with you. So you use the one-time code, get online, do whatever you need, and use the 2FA on the phone the next time.
Usually the setup key is securely stored on the password manager: encrypted database, at least PIN-based security, and so on. Recovery codes are shown on the screen and you have to securely store it, and most of the time they end up on a recovery-codes.txt
, on the desktop. So if one attacker manages to get someone's setup key, the chances are high that he got the recovery codes before that.