The 5870 performed just over 544 Gflops/s in double precision (what anyone actually cares about) while the 6970 does 675.75. That means the 6970 is theoretically 1.24x faster doing nothing but MADs. The 6970 also has more memory bandwidth. With these two factors alone, I'd expect to see a 1.1-1.5x speedup in compute bound applications.
