A 6GB variation of the 780 Ti won't perform any differently than a 3GB variation. There have been hundreds of tests comparing such cards (2GB vs. 4GB versions etc) and even at high resolutions they almost never perform better. Don't believe me?
Let's look at a comparison of a 4GB GTX 770 compared to the base 2GB models running Max Payne 3 and Hitman Absolution, 2 games known to devour VRAM, at 1440p with lots of AA. They perform exactly the same. In fact, for the premium you pay for the extra VRAM you could just as easily get the best 2GB variation with the best 3rd party cooler and overclock it to high hell leading to less of a headache overall.
Here's a similar card from a better source;
a 4GB GTX 680 against a stock GTX 680 with 2GB. Now, the 4GB version edges the stock 2GB version out,
but not really considering it has a 10% core clock OC, there is once again, no difference even at 2560x1600.
The simple fact is, any card that is made to run with 2GB of VRAM, or 3GB, or 4GB, is probably intentionally engineered to run that way. They decided on that amount because it probably means the GPU would choke before the VRAM became a bottleneck, so doubling the amount of VRAM on a 780Ti, or 770, or 680, is NOT going to make a difference regardless of resolution.