@chetan, 6870 is good enough for 1080p. 6850 with 2 GB becomes a little irrelevant because it's a slow card, and wud never cross 1 gb of VRAM in any games. Thus, its better if u go for 6870. And maybe sapphire or MSI, if u r living India, like me .
The HD6870 is the stronger of the 2 GPUs. As jsrudd indicates, you likely won't need the additional video memory at the resolution you are gaming at.
Kind of like comparing 2 cars, one with a more powerful engine and the other with a bigger gas tank. If speed is your primary concern, get the car with the more powerful engine.
Both are good choices. Have fun!
2gb is a waste for a single 6800 card.
If you were running 3 or 4 6850's, then the 2gb version would make more sense.