5870 1GB is approx ~7% slower in 25x16 resolution and ~8% in 19x12.
AMD needs ~26/30% improvement with 6970 at 19x12/25x16 resolutions to basically match 580GTX 1.5GB.
Also your numbers for 6870 are incorrect.
EDIT: I see Vipeax beat me to it.
5870 1GB is approx ~7% slower in 25x16 resolution and ~8% in 19x12.
AMD needs ~26/30% improvement with 6970 at 19x12/25x16 resolutions to basically match 580GTX 1.5GB.
Also your numbers for 6870 are incorrect.
EDIT: I see Vipeax beat me to it.
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