Based on your question you can place these three cards in the following order with one being the lowest.
3. Radeon 6950 2 gb
2. Radeon 6950 1 gb TF3 (Best suited for you)
1. MSI 560 ti TF3 (HAWK)
Also this info is in Best Graphics Cards For The Money: September 2011 article on Tom’s.
Best PCIe Card For ~$185: Tie
GeForce GTX 560 (Check Prices)
Great 1920x1200 performance in most games
GeForce GTX 560
Codename: GF114
Process: 40 nm
Universal Shaders: 336
Texture Units: 56
ROPs: 32
Memory Bus: 256-bit
Core/Shader Speed MHz: 810 / 1620
Memory Speed MHz: 1002 (4008 effective)
DirectX/Shader Model:
DX 11/SM 5
160 W
The new GeForce GTX 560 is, in essence, an overclocked GeForce GTX 460 with optimizations for power. Its improvements make it a great competitor for AMD's Radeon HD 6870. Both boards introduce impressive gaming performance that we simply haven't seen before under the $200 price point.
Read our full review of Nvidia's GeForce GTX 560 for more information on the card and its accompanying architecture.
Best PCIe Card For ~$240:
Radeon HD 6950 1 GB (Check Prices)
Excellent 1920x1200 performance, Good 2560x1600 performance in most games with lowered detail
Radeon HD 6950 1 GB
Codename: "Cayman"
Process: 40 nm
Universal Shaders: 1408
Texture Units: 88
ROPs: 32
Memory Bus: 256-bit
Core Speed MHz: 800
Memory Speed MHz: 1250 (5000 effective)
DirectX/Shader Model: DX 11/SM 5.0
Max TDP: 200 W
AMD dropped half of the reference Radeon HD 6950's on-board memory to give us this 1 GB model, and the price fell accordingly. At $240, there really isn't any competition for this powerful, yet conservatively-priced graphics card. It outperforms the GeForce GTX 560 Ti in enough situations, on average, to score the sole recommendation.
In addition, some users have unlocked shader cores artificially disabled by AMD through a firmware update, transforming this board into an underclocked 1 GB version of AMD's Radeon HD 6970.
Read our full review of AMD's Radeon HD 6950 for more information on the card and its accompanying architecture.
Best PCIe Card For ~$270:
Radeon HD 6950 2 GB (Check Prices)
Excellent 1920x1200 performance, Good 2560x1600 performance in most games with lowered detail
Radeon HD 6950 2 GB
Codename: "Cayman"
Process: 40 nm
Universal Shaders: 1408
Texture Units: 88
ROPs: 32
Memory Bus: 256-bit
Core Speed MHz: 800
Memory Speed MHz: 1250 (5000 effective)
DirectX/Shader Model: DX 11/SM 5.0
Max TDP: 200 W
The Radeon HD 6950 offers similar performance as AMD's previous-generation single-GPU flagship, the Radeon HD 5870. A pair of these cards in CrossFire are a force to be reckoned with, as the company noticeably improved scaling compared to some of its previous efforts.
There's another reason to consider this model. Many folks have had luck modding this board into a fully-functional Radeon HD 6970 through a firmware update. If you can pull that off, the value of the 2 GB Radeon HD 6950 seems pretty clear.
Read our full review of AMD's Radeon HD 6950 for more information on the card and its accompanying architecture.