Length extension attack: SHA-384 has a minor advantage over SHA-512

SHA-384 truncation is better protected against a Length extension attack than SHA-512. In this instance longer isn't necessarily better since SHA-512 has no truncation, so the creation of another message with the same SHA-512 is easier.

When choosing a cryptographic hash functions there a several tradeoffs between SHA-2 as show in this comparison of SHA-2 and SHA-3 Secure Hash Algorithms.