Drediock: I have almost exactly the same system as you: 3GHz E8400 on a GIGABYTE GA-EP35-DS3L MB (I think even the RAM is identical). I just upgraded from an HD4850 to an MSI R7870 GPU. I was not impressed. I can set the GPU to very high antialiasing (4x SSAA) without any fps penalty, but the absolute fps, on certain terrains or with lots of planes/vehicles in view, are not that much better than the old 4850 and sometimes fall to 30 fps. The performance is odd: it is so-so no matter what options I select for eye-candy in AH (except environment, which kills fps). Also, the load balancing between the two cores of the CPU is odd; one pegs at nearly 100% while the other coasts at 25%. With the old card (and old drivers) the second CPU was used more. The 7870 had just as many, if not more, artifacts as the 4850 had, including z-fighting (seeing the interior textures of distant barns when you should be seeing the outside, seeing the road through maprooms etc.) The only good thing the R7870 has going for it is it is much cooler and quieter than my old 4850 (it's pretty much silent compared to my case fans).
So I guess this would be a negative recommendation for the R7870.
[grass off, detail range max, object detail max, bump map on, environ. map off, shadows on, smoothed, 4K, shadow others off, detailed water and terrain on, bump map terrain on, water reflection on, bump map buildings on, bump map other vehicles on, buildings cast shadows on. CCC 12.8 (downgrading to an older version actually lowered fps by 6%).]