I would like to know which graphics card is better to buy for the long run AMD Radeon HD 6850 OR 6870?
i would consider having the GPU's in crossfiremode if i have to
(the graphics card will run on ASRock 890GX)
Overclocking is the key. If you plan to overclock, both cards run neck and neck. That's because both will reach the same clock speeds, around 1ghz. If you don't plan on pushing your card towards a maximum overclock, get the 6870.
The CPU will be the AMD Phenom 1055T x6. The resolution will be 1920x1080.
I dont know why you need to know on what resolution the pc will run?
Because that is the first major concern you look at when you are picking out a new GPU.
Higher resolutions benefit from the faster/higher end cards, where as lower resolutions don't benefit so much, and the CPU raw performance is also a consideration, more so at lower resolutions especially.
When you shop for tires, you buy tires to fit the car or truck, you don't just go out and spend $2500 on grand prix racing tires to put on the wife's mini van. You buy what fits the need and your budget.
And since you are asking to help you pick what fits your need, we need to know the rest of your hardware and what you plan on doing with it.