In short, if I use Armory's SWEEP feature I move both my 10 bitcoins and the Coinbase.com private keys to my Offline PC for cold storage.
If you use SWEEP, your coinbase.com private keys stay with coinbase, but your bitcoins are now associated with private keys in your Armory wallet. Only you can spend the money, using Armory. This is what you want.
However, if I use Armory's IMPORT feature I move only my 10 bitcoins and the Coinbase.com private keys remain behind with my Coinbase.com wallet.
If you use IMPORT, then your bitcoins remain associated with your coinbase.com private keys, but these private keys are now available BOTH in coinbase and in Armory
I'm a newbie, but the way I see it if Coinbase.com remain with control of the private keys to my 10 bitcoins they can in the future illegally use my bitcoins if they were to get hacked.
Therefore, if I understand the SWEEP feature correctly, it's better to use SWEEP when transferring bitcoins from Coinbase, Blockchain.info, Circle, etc. Because using the SWEEP feature assures Coinbase, Blockchain.info, Circle, etc do not remain in possession of private keys that can be used illegally if hacked.
Exactly! You understand it correctly.
An alternative to sweeping which is probably easier is to just send you BTC from you Coinbase.com wallet to your Armory wallet. Get a bitcoin address from Armory, copy-paste it into the coinbase wallet. It does exactly the same thing.