Why might SHA-384 throughput be lower than SHA-512 throughput in hashcat and more secure? I found a hashcat benchmark results in the internet: hashcat results:


SHA-384 is 17065.4 MH/s
SHA-512 is 17280.3 MH/s


Why does SHA-512 take less time? SHA-512 is longer and I thought it therefore needs more time and computation resources to compute the hash?
The only differences in calculations are the initial value and the output size. From NIST FIPS 180-4


The initial hash value, $H^{(0)}$, shall be set as specified in Sec. 5.3.4; and
The 384-bit message digest is obtained by truncating the final hash value  $H
^{(N)}$, to its left-most 384 bits:
$$H_0^{(N)} \mathbin\|H_1^{(N)} \mathbin\|H_2^{(N)} \mathbin\|H_3^{(N)} \mathbin\|H_4^{(N)} \mathbin\| H_5^{(N)}$$


When two source codes are compared inc_hash_sha384.cl and inc_hash_sha512.cl one can see that actually, SHA-384 does less job than SHA-512. It is not coded simply truncate the SHA-512 with different initial values. For the little speed difference, one explanation can be the vectorization that helps SHA-512 during the final calculations.
In the case of password protection, the tiny difference does not make much difference. In password hashing, actually, we use specially designed password mechanisms like PBKDF2 and Argon2 which was the winner of the password hashing competition.
In the security perspective, SHA384 has resistances to length extension attack but SHA512 doesn't have. SHA384 has 128-bit resistance against the length extension attacks since the attacker needs to guess the 128-bit to perform the attack. This is due to the truncation.
The different initial value provides domain separation. With domain separation  $$\operatorname{SHA384}(m) \neq \operatorname{SHA512}(m)|_{384}$$ where $|_{384}$ is the truncation.
In the case of pre-image, secondary pre-image, and collision resistance in generic attacks we have;
\begin{array}{|c|c|c|c|}\hline
&amp; \text{pre-image resistance} &amp; \text{2. pre-image resistance} &amp; \text{collision resistance} \\\hline
\operatorname{SHA-384} &amp; \mathcal{O}(2^{384}) &amp; \mathcal{O}(2^{384}) &amp; \mathcal{O}(2^{192}) \\\hline
\operatorname{SHA-512} &amp; \mathcal{O}(2^{512}) &amp; \mathcal{O}(2^{512}) &amp; \mathcal{O}(2^{256}) \\\hline
\end{array}
The collision resistance is $\mathcal{O}(\sqrt{2^{n}}) = \mathcal{O}(2^{n/2}) $ due to the generic birthday attacks.
Therefore; SHA-512 is better in the case of pre-image, secondary pre-image, and collision resistance.  SHA-512's only weakness is that it is prone to length extension attacks.