I want to mention I read everyones posts before saying anything, because clearly people don't do that. I also researched before posting anything.
The first thing that is important (for me) to know is what resolution are you running, and are you using any form of anti-aliasing? Personally, I leave AA on low settings, but turn everything else to ultra. Why? Because I don't have perfect vision, and so I can't see the quality difference with AA on or off, but I do see the benefit of ultra settings (Such as on Skyrim).
No one here mentioned to you that using SLI / Crossfire can be a pain, and that in general, single card solutions are simpler and easier. Oh, and I agree that your CPU is likely hurting your FPS, you might consider reading this:
http://www.tomshardware.com/reviews/athlon-l3-cache,2416.html "Finally, it remains to be said that L3 cache memory is imperative if you want to reach the highest performance levels." - Second last sentence in that article.
A couple people (Dalauder for one) made some unfortunate mistakes. He said "there is NO AMD CPU that will give you 60fps in all games (at stock speeds)". Frankly, that's unfair, because if you look at Metro 2033 (
http://www.tomshardware.com/reviews/sandy-bridge-core-i7-2600k-core-i5-2500k,2833-18.html ) you can see 2 AMD CPUs (both will work with your motherboard, I checked the product page) that can get an average of over 60FPS, even though Metro is a VERY demanding game (They had AA on). The most powerful GPU they used is a GTX 580 in those tests. Also, if you ranked it from which CPUs had the highest minimum FPS, AMD gets 1st and 3rd place. I mention that because to me, lowest FPS is more important than average.
Start Edit 2: Clearly Delauder is even more ignorant than I thought. He said that no AMD CPU can get over 60 FPS in BF3... Well,
http://www.tomshardware.com/reviews/gaming-fx-pentium-apu-benchmark,3120-4.html says that even an OCed i5 2500k (4GHz) with an AMD 7970 CAN NOT get avg 60 FPS, yet the general consensus is that the i5 is the most powerful CPU you need for gaming. Also you will notice that on page 3 of that article is the Skyrim benchmark. Don't go by that as being the average now, but because Skyrim and BF3 has since been patched to greatly improve performance, consider that the lower bound of what you can get. In reality, those games do far better today than they did when that review was published. It just goes to show that even unpatched, AMD does fine.
End edit 2.
I run a 1090T (at stock) with a 6950 TF2 (Factory OC only) and I get usually around 50FPS (using MSI afterburner) on Metro 2033, and I am always hitting the 60FPS cap in Skyrim, both games turned up to Ultra / max.
I'm not sure where you live, so I checked newegg in Canada and the US: The AMD 965 BE $120
http://www.newegg.com/Product/Product.aspx?Item=N82E16819103727
Change the .com to a .ca to search it in Canada. In the US it is free shipping, in Canada, $6 shipping.
Why the retail and not OEM? This way you can sell your current CPU (with heatsink, because it is more valuable that way) and you don't have to buy new thermal compound.
That CPU should be more than enough for 1080p, and is easily OCed (go OEM with aftermarket cooler for high OCing, but you can easily get another 200MHz without even changing voltages). That CPU and your current GPU should be more than enough for now, and, when more high end GPUs are released (that is, more 6xx series cards) then you can sell your GPU and upgrade.
Edit: Fixed broken link