Vulkan itself is technically superior, however Valheim is a DX11 game and any other one used is using analogue features - vulkan can't shine if it's advanced features aren't utilised. Same if you have DX12 hardware & software - doesn't matter, it's a DX11 game.

So, there should be no difference. However hardware/driver differences may see one outperform the other.

Personally I find vulkan chokes less on snow & portal lighting - especially the combination of the two. Win10, i5-12500 & 3070ti, so not gold plated but no slouch.