I want to know difference of calculation cost between SHA(hash) and AES(reversible encryption)
With AES/CBC mode, an attacker can modify the string, and have the result decrypt without errors; the only thing that can cause a decryption failure is an illegal padding pattern after decryption, and:


If the plaintext string is at least 17 bytes long, then the attacker can modify the string without affecting the padding bytes (and thus leave a valid padding pattern)
Alternatively, changing the entire ciphertext randomly leaves a 1/256 chance that, after decryption, the last byte of the ciphertext is 01 (which is a valid padding pattern)


Hence, to answer your question, HMAC-SHA256 is the best answer, as AES doesn't do the job at all.  If your crypto toolkit provides it, you might want to consider AES-CMAC instead (which is another right answer for this problem)