Performance at the AMD Radeon HD 7870's stock speeds isn't particularly spectacular. Compared with the HD 6970 there isn't a lot of extra performance in the newer silicon. In certain cases the older card actually takes a bit of a lead.
That said in the very niche field of tessellation, in both OpenGL and DirectX 11 APIs, the HD 7870 takes the previous generation to task.
Thanks to the massive amount of performance headroom AMD has deliberately left these chips with you can push them well over the already high reference clock to something that will make the more expensive Nvidia cards sit up and take notice.
When you can rival the competition's top single-GPU card with your mid-range card then you know you're doing something right.
DirectX 11 tessellation performance
OpenGL tessellation performance
DirectX 11 gaming performance