In terms of overall gaming performance, the graphical capabilities of the AMD Radeon HD 7950 PowerColor PCS+ Edition are massively better than the Nvidia GeForce GTX 560.
The HD 7950 has a 70 MHz higher core clock speed and 56 more Texture Mapping Units than the GeForce GTX 560. This results in the HD 7950 providing 53.2 GTexel/s better texturing performance. This still holds weight but shader performance is generally more relevant, particularly since both of these GPUs support at least DirectX 10.
The HD 7950 has a 70 MHz higher core clock speed than the GeForce GTX 560 and the same number of Render Output Units. This results in the HD 7950 providing 2.3 GPixel/s better pixeling performance. However, both GPUs support DirectX 9 or above, and pixeling performance is only really relevant when comparing older cards.
The HD 7950 was released less than a year after the GeForce GTX 560, and so they are likely to have similar driver support for optimizing performance when running the latest games.
The HD 7950 has 2048 MB more video memory than the GeForce GTX 560, so is likely to be much better at displaying game textures at higher resolutions. This is supported by the fact that the HD 7950 also has superior memory performance overall.
The HD 7950 has 111.9 GB/sec greater memory bandwidth than the GeForce GTX 560, which means that the memory performance of the HD 7950 is massively better than the GeForce GTX 560.
The Radeon HD 7950 PowerColor PCS+ Edition has 1792 Shader Processing Units and the GeForce GTX 560 has 336. However, the actual shader performance of the HD 7950 is 1419 and the actual shader performance of the GeForce GTX 560 is 544. The HD 7950 having 875 better shader performance and an altogether better performance when taking into account other relevant data means that the HD 7950 delivers a massively smoother and more efficient experience when processing graphical data than the GeForce GTX 560.
The HD 7950 transistor size technology is 12 nm (nanometers) smaller than the GeForce GTX 560. This means that the HD 7950 is expected to run slightly cooler and achieve higher clock frequencies than the GeForce GTX 560.
The GeForce GTX 560 requires 150 Watts to run but there is no entry for the HD 7950. We would recommend a PSU with at least 500 Watts for the HD 7950 and a PSU with at least 450 Watts for the GeForce GTX 560. The HD 7950 has been recommended a PSU with 50 Watts more than the GeForce GTX 560. The difference is significant enough that the HD 7950 may have a slight adverse affect on your yearly electricity bills in comparison to the GeForce GTX 560.