DX9 is fundamentally different than DX11. It's an older API and it puts a larger load on the CPU while DX11 offloads more to the GPU. This means that more demanding games will usually perform better in DX11 mode than DX9 when coupled with a DX11 compliant graphics card.
^What pinhedd said. Keep in mind that dx updates add features and optimizations. Sometimes the features you turn on, better shadows more detail etc., will cause the game to run slower and sometimes the optimizations make it run faster.