I think you are throwig the term bottleneck around too much in your posts. Something will always be limiting your fps whether it is your cpu or your gpu. Some games your processor will hold you back and some your gpu will. I would get whichever one you feel like buying. If you want to spend more then 7870 if not 7850.
 

skitz9417

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so one in aother thead told me this I would suggest upgrading the cpu to the fx 4320 or the fx 8150 (if you have the money for it) and then get a new 1920x1080p monitor. You will still get a good frame rate, but some settings would have to be turned down a bit, unless you want to overclock it. You can get 7850 to a 7870 performance easy and then some
 
Well, I can't really go on detail which games would bottleneck and which isn't. But when I said it's 'fine' it means that most games you won't feel the bottleneck. Yes upgrading on to an FX-43xx is better, but I think for now, you should be fine on the 840.