Difference between transfers

"Copy an account from another server with account password" should only be used when "Copy an account from another server" does not or cannot work (due to lack of root access). It's essentially not as good but can become useful in situations where you are root on a user and are transferring from a server on which you do not have root access.

In these situations however, I would recommend just using the account backup feature on the server you don't have root on then uploading/importing that on the server you do have root on.