I have been looking for a new gaming computer for quite af while, and i have found two, who cost about the same.
My problem is, that i do not know which one to choose
I am really aiming for the best gaming experience.
The Athlon II X4 will do pretty well in gaming, i would take it in combination with the GTX 560 over the Phenom II X6 in combination with the 6850 especially if you plan to game at higher resolutions. The higher the resolution the more likely the GPU is to be the determining factor, and either of those CPUs can put out playable frame rates so the only thing that will be causing you a noticeable difference will be the graphics card and how high you can turn up the settings.
If you are only playing at 1280x1024 you are going to be running into a CPU bottleneck on both of them because that resolution isnt going to stress either of those GPUs too hard, even at higher settings. In that scenario the second one would put out better frame rates from the stronger CPU but unless you are tracking it with FRAPS you wouldnt be able to tell the difference, at 1920x1200 the first system would do better than the second one and it would actually be noticeable.