I'm using paper wallet now for cold storage and blockchain for everyday use.
Which site paper wallet you are using
There is no relation between paper wallets and other wallets, paper wallet is a wallet but it is usually misunderstood as there are many ways to create it and most of them prefer to do it online but it is depreciated as it destroys the real use of paper wallets and is less secure.
I recommend you to use bitaddress.org offline version or use other offline paper wallets generator to secure your Bitcoin.
-MZ
You are confusing paper private keys with paper wallets.
Using a JavaScript client to generate these paper private keys (like BitAddress) is a bad idea (even offline), because of the lack of true randomness.
If someone wants to use paper wallets, I think the best chocies are Armory, mSIGNA (btw, I didn't see any mention to mSIGNA here, although it's endorsed at Bitcoin.org. Nobody at least tried it?) and Electrum. If you don't want a wallet to this, just a generator, Bitcoin Address Utility can match this.
https://en.bitcoin.it/wiki/Bitcoin_Address_Utility