Unfortunately, the SHA cpu extensions that will soon be available in Skylake Xeon parts (and the crypto extensions in ARMv8-a) only support sha2-256 (and SHA256/224, and the ill-advised sha1... why is Intel adding instructions or microcode for a hash function that's being phased out?). So you have a choice between a faster-in-software-on-64bit sha-512/256 and a faster-in-hardware sha-256. Unless there's some way to get partial speed-up of sha-512 using sha-256 instructions, but at a glance they don't look low-level enough to apply to sha-512... do they?

Or you can ignore both sha256 and sha512/256 and use something else like sha-3 or blake2b. Blake2b obviously has less attention on it so more likely to harbor a weakness, but it's fast in software. And sha-3 will get cpu extensions eventually, and it'll hopefully be a better thought out inplementation than just support for the 256-bit variant.