Overclockers Club published a review on the Ashes of the Singularity: Escalation - DX12 & Vulkan Short Analysis A quote from the article:

When I initially had the idea to do these tests, I had no real expectations as I just wanted to see what the results would look like. I also did not have the Vega 64 at that time, but thankfully it actually arrived the same day the v2.4 patch did, so I could do some runs with it. I truly did not expect any significant impact by using Vulkan instead of DirectX 12, but that is what we are seeing here for both GPUs. Looking at these benchmark results, which are admittedly synthetic, it seems it is best to keep to DX12 for the GTX 1080, as it saw a drop in performance, even though the CPU frame rate increased. The driver overhead also became more consistent with Vulkan, but if it does not manifest as better performance, there is little point. Of course, this may change with updates to both the game and the drivers. On the Vega 64, however, switching to Vulkan improved performance, even if the driver overhead also increased. Average frame rate and CPU frame rate increased under the newly-added API for this recently released GPU, so it is possible we could see further gains here in the future.

 Ashes of the Singularity: Escalation - DX12 & Vulkan Short Analysis @ OCC