Vulkan> DX12.
Both are AMD and Nvidia are getting gains on Vulkan. However, on DX12 only one party wins.
Comparision ain't really fair though. Doom graphics are tuned for high fps, so you are more likely to run in cpu bound scenario, than you are on lower fps in tomb raider for example. If this game was done with DX12 instead of Vulkan, I expect gains would have been similiar.