No one should be using Google Authenticator tbh. It doesn't backup your keys at all. Even if you backup all the data on your phone, e.g. via iCloud.
So if you accidentally drop your phone and have to send it off for repair, you'll lose access to all of your accounts. It's not too much of a problem if you kept all the recovery keys, but I'm betting the average user will either end up losing those or not bothering to save them in the first place.
If you use Google Authenticator please - make sure you have your recovery keys printed out, or just move to Authy which does backup your auth codes. You may be able to tell I'm speaking from experience...
Uum, literally right from their update change log "The update brings with it the ability to search for accounts and transfer multiple accounts to another device,"