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Synthetic testing
Yes, yes, I know you're dying to get into game benchmarks. However, synthetic benchmarks set the stage for everything else, helping to demonstrate how well the theoretical peak throughput numbers we've discussed translate into delivered performance.

Texture filtering

  Peak bilinear
filtering
(Gtexels/s)
Peak bilinear
FP16 filtering
(Gtexels/s)
Memory
bandwidth
(GB/s)
Radeon HD 7770 40 20 72
Sapphire Radeon HD 7790 56 28 102
Radeon HD 7850 1GB 55 28 154
MSI GeForce GTX 560 Twin Frozr II 49 49 134
Zotac GeForce GTX 650 Ti 2GB AMP! 66 66 99

In the real world, memory bandwidth plays a part in texturing performance. That probably explains why the Radeon HD 7790 falls behind the 7850 1GB here.

Tessellation

  Peak
rasterization
rate
(Mtris/s)
Memory
bandwidth
(GB/s)
Radeon HD 7770 1000 72
Sapphire Radeon HD 7790 2150 102
Radeon HD 7850 1GB 1720 154
MSI GeForce GTX 560 Twin Frozr II 1760 134
Zotac GeForce GTX 650 Ti 2GB AMP! 2066 99

Wow. The 7790's two geometry engines do wonders for tessellation performance, especially when paired with a 1075MHz core clock speed, as on the Sapphire card.

Shader performance

  Peak shader
arithmetic
(TFLOPS)
Memory
bandwidth
(GB/s)
Radeon HD 7770 1.3 72
Sapphire Radeon HD 7790 1.9 102
Radeon HD 7850 1GB 1.8 154
MSI GeForce GTX 560 Twin Frozr II 1.2 134
Zotac GeForce GTX 650 Ti 2GB AMP! 1.6 99

The 7790 comes out on top here.

We'll have to stop our theoretical explorations here, unfortunately. I normally include LuxMark, an OpenCL-accelerated ray-tracing benchmark, in this set, but it refused to run using the drivers AMD provided for the 7790. Oh well; moving on...