I previously asked if I would be able to enjoy this game. I ended up downloading the demo and I played a small portion of it and was actually shocked at how well it run.  
 
My question now is pertaining to the direct x version I should play. When I started up the game it said run in Direct x 9.0 or Direct x 11 - Recommended(I think it actually said Direct x 10/11, but I don't know if that makes sense). i chose the recommended option. I'm wondering if I chose direct x 9.0 would it run even better? Is the main difference quality of graphics vs. speed of the game? 
 
Thanks in advance

This is an issue that is extremely dependent on your computer. One configuration can run completely different than another. Both hardware and operating system can easily throw off how your installation works compared to another. The best advice I can give is try both settings to see which you like better. 
 
My experience has been the same as Zurv's: DX10/11 looks and runs better than DX9 mode.

Just to let you know, the demo run in DX9, not 11, so should any problems arise if you decide to try out the DX11 version, jump back to 9 to see if it fixes it.

What gpu are you running? If it's DX11 compatible and you have vista or windows 7, I recommend you use that setting if your card can handle it.  
 
I don't have the game myself, however from the screenshots the DX11 looks sharper, less jaggies and has better textures on the ground, also reflections in the water.

 11 
-  9 
   2 
 
The difference is 2.

" 11 
-  9    2  The difference is 2. "

i was able to run civ 5 in dx 9 mode with 1366x768 res. with all the other settings set to low. It ran good enough, and its pretty funtoo. i cant wait to play the demo on my home PC.... itll look awesome

For me with a NVIDIA 8800 GTS video card the difference between DX9 and DX10/11 is that I can play the game in DX9, but I cannot play the game consistently in DX10/11 without frequent crashes :( 
 
Come on Firaxis.  Put out a patch for us 8800 users!