Big enough to make the additional cost worthwhile
Guru3D uses the following games in their test suite, COD-MW, Bad Company 2, Dirt 2, Far Cry 2, Metro 2033, Dawn of Discovery, Crysis Warhead. Total fps (summing fps in each game @ 1920 x 1200) for the various options in parenthesis (single card / SL or CF) are tabulated below along with their cost in dollars per frame single card - CF or SLI:
$ 140.00 6850 (371/634) $ 0.38 - $ 0.44
$ 160.00 6870 (434/701) $ 0.37 - $ 0.46
As you can see, the 6870 has a lower cost per frame at 37 cents....not quite the purported double frame rate as reported above but it is 17% faster for just a 14% increase in cost which is a sound return on investment in my book.
OP asked 6750 versus 6870, not 6850 versus 6870. The 6870 is clearly shown to be almost exactly twice as fast as the 5750 in the review that I linked (anand is a very reputable source) and the 6750 is equal to the 5750, so the 6870 should be almost exactly twice as fast as the 6750.