The Vram does not set how fast your card is it helps when you have more than one monitor or your resolution is more that 1920 x 1200. Unless you are doing what I just stated then I would get the 560 ti.
So here is a link the 6870 vs the 560 ti in SLI/CF. One more thing since the cards are so close if you are using higher graphics or more than one monitor then if it is cheaper then get the 6870. I hope this helps and good luck to you.http://www.anandtech.com/bench/Product/301?vs=441