Directx 9 or 11?

[DragonRider]

Hello!

This questions has bothered me alot: do games run smoother on DirectX 11 that on DirectX 9?

Let me give you more info about my system.

Windows XP Professional SP3
PC: Intel Pentium Dual CPU 1.80GHz
2.00 GB or RAM
Video card: Radeon X1600/1650 Series 256mb RAM

Yeah, my PC is a little bit old.
Now I know that Win XP only supports DirectX 9. But teoretically, if I install Win 7 and use DirectX 11 will my games run better/smoother on this PC?

Note that I only play games that can run on my system. So Borderlands 2, for example, is out of the question.

Thank you in advance!