Vulkan will (and not might) give better performance, not because it's better than dx12 (it's not) but because
SC run on dx11. It's a generational gap. Vulkan and DirectX 12 have better support for multiple threads to send commands to the GPU simultaneously. And with Vulkan you can send commands directly to the GPU, bypassing the CPU. Rendering in SC is limited by CPU on a lot of systems in its dx11 version.
On games not optimised for Vulkan you gain some fps :
here or
here
But on games only made to use Vulkan, graphic intensive and tuned to use effectively the multithread capacity of Vulkan and direct GPU access, there will be a boost from dx11. And for what I've read from the devs, that's what they work for.
For now, it's hard to give a real dx11 vs vulkan comparison because games really using the vulkan capacities are rare and for most of them, they where not switching from dx11. For me SC will be the first where we will see this switch.