you don't gain any additional security for using different addresses. you can gain privacy if you buy each coin from different sources.
I would argue that you do gain security somewhat if you have multiple of these and putting them in different locations. So that when a fire does happen, only one is destroyed.
in my experience it is best for me to encrypt one paper wallet and remember 1 password (the pass used for encryption) and store that in multiple places instead of having multiple un-encrypted paper wallets spread in different places because it would be impossible to encrypt and remember all their passwords!