It doesn't matter so much about which version of DirectX you have installed, and more about which games support it, and what extra features DX11 adds to the game. In some circumstances, DX11 actually improves performance, like World of Warcraft's application of it, where no extra eyecandy is added, but it works more efficiently than the DirectX 9 codepath. Most of the time, you will likely get better framerates with DX10, as it doesn't have as many features that heavily tax graphics cards. Tessellation and Advanced Depth of Field tend to really pull the framerates down. Compared to DX10, I don't think DX11 is all that more efficient, in Metro 2033 I didn't see much difference between DX10 and DX11 with its extra features disabled as far as framerates go.
There are very few games that actually support DirectX10 and DirectX11, off the top of my head the only ones I can think of are Metro 2033, and the upcoming Battlefield 3. Most of the time if a game supports DirectX11 it also supports DirectX 9, to ensure compatibility with Windows XP. DX9 will usually give you better framerates simply due to the fact that there is less eyecandy that can really stress your GPU, World of Warcraft being one of the few exceptions.