The password is used to encrypt your private key. When you change the password, the client decrypts the private key using the old password and then re-encrypts it using the new password, overwriting the old file in the process.
What this means is that if you have a backup of the encrypted key, you can always unlock that key with your old password. That is the safest way to update the password. Back up your keyfile, then use the password update command. Worst comes to worst, you just re-import the backup. Once you've verified that the password update was successful, you can delete the backup.
I'd say that in all, this method is a safer way to update your password. Sending fund requires a transaction fee and there's always the chance of a typo.
If you're not sure how to make a backup: How do I backup my ether accounts?