When you don’t see similar gains then you probably didn’t set it up right. The numbers you describe seem to be “DirectX11 over OpenGL” versus “DirectX9 over OpenGL”, meaning, you’re running with a vanilla WINE installation, but haven’t got DXVK installed and set up.
If you want to know how to set up DXVK with WINE, then see here:
If you want to go with Steam Play / Proton then you’ll find a list of steps here:
The whole effort around Vulkan and using it for DirectX is still young and is seeing lots of fixes and further development currently. Best chance for a quick’n’easy installation will likely be Steam Play / Proton, because it entails it all as well wraps it nicely into Steam, which makes it available for a lot of other games, too.