D3D9 has a definite performance increase over D3D8 - without changing anything else, it made me stop dropping frames around Merissas, in certain annoying parts of Desert, etc. I've heard some reports of D3D11/12 further improving frametimes and stuttering over D3D9, but it didn't do anything noticeable for me.
Also, with D3D9 or above, you can use all of the new fancy antialiasing options.