Using a truncated SHA-512/256 also has the advantage of being considerably faster than SHA-256 on 64-bit CPUs. The performance difference is close to 50%. As such, I see no reason to use SHA-256 for anything[1], you're better off just using SHA-512/256 as the net storage is the same as well (32-bytes).
[1]: Assuming you're running on a 64-bit platform...