It could cause all those things. DX11 is supposed to bring 'greater' graphics and better use of newer hardware.
Coding of games with dx11 will start using multi cores and new gpu features ,such as tesselation.
So your gpu is working harder, and maybe the game engine is asking more of your cpu ?
I don't know, don't have that game.
I will give you a example of another game doing this, F1 2010- dx9 runs at over 80fps with my 460sli , with dx11 patch , its about 60fps.
But its very pretty