Hi Tony,
Unfortunately, loading configuration between models is not supported. I would recommend to get them both to the same OS revision (including the minor version), and join them in a cluster. Centralized Management feature is now part of basic functionality and does not require an additional license to be purchased. Create the cluster on the C160, configure networking on the C380 and join it, and your configuration will sync. Finally, shut down the C160, remove C380 from the cluster (it will flatten the configuration back to a single machine mode), and assign it the IP addresses formerly used by the 160.
Feature keys are tied to the device, loading configuration from a different S/N will not load the feature keys. They will be available once your appliance connects to the Internet. You should have also received a license file ("PAK") from Cisco as you purchased your new appliance. If desired, you can manually import keys in the PAK file onto the appliance.
Hope that helps!