I've noticed a number of games lately that give me a choice of what version of DirectX to run the game with, usually 9, 10, or 11 (or some subset thereof). I have a graphics card that supports DirectX 11 (AMD 6750M, but it shouldn't really matter for this question), but I've noticed that some games still recommend using the older version of DirectX when I use whatever 'detect hardware' optimal graphics settings the game suggests. Further, in some games, I've actually noticed a significant improvement in FPS after switching to the older version.
In general, is there a rule of thumb for determining which version of DirectX I should be using? Is there any reason this option is even given, rather than just automatically using the newest supported by whatever video card is available?