Difference between encrypted backup of an encrypted DB and an unencrypted backup of an encrypted DB

As per books online

"The is_master_key_encrypted_by_server column of the sys.databases catalog view in master indicates whether the database master key is encrypted by the service master key."

Here is the link http://technet.microsoft.com/en-us/library/ms174382.aspx

It's possible to move a private key from one server to another, if the symmetric key was created using a certificate. The certificate is what allows you to create the same symmetric key on a different server. Looks like that is your approach so you are off to a good start. You have created a symmetric key, secured with a certificate, to encrypt a column of data. To move a symmetric key to another server, you need to follow the following process:

1. You need to back up the certificate and move this to the other server. To do this, use the BACKUP CERTIFICATE... WITH PRIVATE KEY command. Note that this creates two files: the certificate itself, and its private key file.

   BACKUP CERTIFICATE sales05 TO FILE = 'c:\storedcerts\sales05cert'
   WITH PRIVATE KEY ( FILE = 'c:\storedkeys\sales05key' , 
   ENCRYPTION BY PASSWORD = '997jkhUbhk$w4ez0876hKHJH5gh' );
   

2. When you create the certificate on the destination server, you specify both the certificate file, and the private key file, along with the password you used to back up the certificate on the source server. Here is the example from MSDN:

   CREATE CERTIFICATE Shipping11 
   FROM FILE = 'c:\Shipping\Certs\Shipping11.cer' 
   WITH PRIVATE KEY (FILE = 'c:\Shipping\Certs\Shipping11.pvk', 
   DECRYPTION BY PASSWORD = 'sldkflk34et6gs%53#v00');
   

Once you have the private key over to the destination server, you can create a symmetric key using the certificate, and decrypt your columnar data using this.

It's not necessary to move the master database key from server to server, however, you do need to have a master database key created on each server. The master key is needed to protect the private keys internally, and to support server bare metal recovery. You don't need the master database key password to copy a certificate. It's the certificate that you need, and you should be able to access this as sysadmin, unless the certificate itself is protected locally, in which case you'd need the certificate's creation password to run the BACKUP operation above.