Titan,
the 5570 is basically an 5670 with DDR3 memory, and also greatly downclocked. Ergo, that chip was designed to run on ~800MHz yet its set down to 650 by factory default. In the other hand, the 6870 is nearly the maximum what the Barts chip knows - dont expect any wonders.
Also, in a mixed-limit situation (AH with high settings) if youre overclocking the GPU, it wont greet you back in the FPS. You have to find the actual bottleneck (CPU? which part of the CPU? GPU core? V-ram?) and only increase the required clock. For example, i have a phenom955-5830 combo, with the shadows turned off, increasing the GPU clock wont take any effect - the CPU core and the L3 cache is the limiting factor. With all the settings turned on, it becomes more GPU-limited though.