Which Authenticator?

Q u o t e:
I know they both protect but does either have any benefit over the other?

I suppose that depends. As you said both versions do the same thing. The difference would be the device itself. With a physical Authenticator you have an item that you can carry with you, attach to your keyring, etc. . . . the battery itself is estimated to last for many years.

It does come with a risk of losing it though.

A Mobile Authenticator works the same way but it is dependent upon the phone you use and it's operating system. If you upgrade the phone or it becomes corrupt and needs to be reset you can lose the specific "authenticator" that you have on your phone, which will prevent you from being able to log in.

In either case if you need to remove the Authenticator and no longer have access it you can contact our Billing department. If you are able to identify yourself as the registered user on the account and you can provide the serial number for the Authenticator they can help you over the phone. If you do not have this information you will likely be required to send in ID verification before it can be removed.

This can be an inconvenience but to allow the easy removal of the Authenticator without proper verification would defeat the purpose of using such a device.

More information on both can be found in the following links.

http://us.blizzard.com/support/article.xml?locale=en_US&articleId=26109
http://us.blizzard.com/support/article.xml?locale=en_US&articleId=24660

I hope that helps. :)