I'm going to talk about Vulkan because it's basically the same thing (At least as far as any AMD engineer is concerned, cough) and that's what Dolphin supports.
For Dolphin, Vulkan runs a good deal better on AMD than OpenGL, our default. Probably better than D3D11 as well but after D3D11, you're splitting hairs at that point. You're likely already full speed so whatever.
For games, I haven't seen any titles not on AMD that performs better on D3D12. Mostly because engine devs can't seem to beat how fucking efficient nvidia's D3D11 drivers are. (since D3D12/Vulkan is just 'do the work yourself')
Finally, it really depends what GPU you upgrade to. A low end current gen card is going to be slower on any API than a current gen high end card on any API.
For Dolphin, Vulkan runs a good deal better on AMD than OpenGL, our default. Probably better than D3D11 as well but after D3D11, you're splitting hairs at that point. You're likely already full speed so whatever.
For games, I haven't seen any titles not on AMD that performs better on D3D12. Mostly because engine devs can't seem to beat how fucking efficient nvidia's D3D11 drivers are. (since D3D12/Vulkan is just 'do the work yourself')
Finally, it really depends what GPU you upgrade to. A low end current gen card is going to be slower on any API than a current gen high end card on any API.