Once your coins are moved to a paper wallet, they're no longer held by Coinbase. As with any paper wallet, safety of the coins becomes your responsibility alone. You'll need to import them back into a wallet (Coinbase or any other wallet) to spend them.
A printed backup (blockchain.info, etc.) is different from a paper wallet, in that the wallet still has the keys, i.e. they are not off-line or in "cold storage".
The only way they wouldn't be safe was if someone got your private key(s) during the paper wallet creation/printing process. This has been discussed extensively elsewhere on these forums.
But coinbase still has to move them to a hd or somewhere. They say they distribute them all over the world, so its still under their control. I guess the only way to be almost 100 percent sure/safe way is to have armory and put it on a thumb drive with a paper wallet then disconnect from the internet..
Im not sure that coinbases security is that good. Im sure its okay, but I guess nothing is going to be 100 percent foolproof..
Not true. Quote from Coinbase:
A paper wallet is not a backup
Any bitcoins sent to your paper wallet will no longer exist in your Coinbase account — they will only exist in the wallet. Consider this an export.
Sounds like what they do is generate a new Bitcoin address with a new private key and transfer the coins. Then they convert it into a paper wallet. From that point on, you can no longer access those coins from coinbase.com and the only way to spend them would be to import that paper wallet. It would be the same thing you would get from an Armory paper wallet except there would be no digital copy so if you lose that paper wallet you're SOL.
Another thing, judging solely on the paper wallet is that I would trust Armory a tiny bit more because the private key would never travel through the internet (and if Coinbase wanted to be malicous they could store a copy of the private key before they sent it to you and be able to run off with your money at a later date.)
