Comparing Bip 38 to AES256 Can anyone explain what are the advantages of using BIP 38 Bitcoin wallet encryption to simply encrypting the private key with AES256?
See the following links for an overview and for details.

Note: In short, if you do not have a strong understanding of the BIP38 encryption and decryption workflow, do not BIP38-encrypt your paper wallet. Just print your paper wallet out without encryption, and keep it safe the same way you would jewels or cash.

Just encrypting with AES provides excellent security but the weakness is the key which is unwieldily since it needs to be random binary data and the encrypted output which is also binary data. In order to use a passphrase as the encryption key a function such as PBKDF2 is generally used and the output can be base64 encoded to make it ASCII so it can be printed/written. Finally, unless you are a crypto domain expert do not roll-your-own security schemes, they generally will contain flaws rendering the security null.

Note: Scrypt is a form of Password-Based Key Derivation Function (PBKDF2) that has increased memory requirements.

BIP38 encryption provides the above and some inter ability with the crypto currency eco-system.