More v-ram is always a good thing and the 2gb model will do a little bit better than the 1gb , but if money is tight then you can play the game with the 1gb model. The one thing that you should consider is that when you buy the card , then that's the card you will have untill you get another and once you get it if the financial situation changes then you are stuck with that card. If you get the 2gb version then you won't have to think about whether or not you should have got it if you come accross some extra money.
Im not sure having more v-ram is always a good thing, its not a bad thing, but having more than you need is a waste of money. From everything that ive read and benchmarks ive seen so far, 2gb is really only beneficial at very high resolutions (over 1080p) and/or multi screen setups.
I play bf3 on high at 1920x1080 with a 1gb card (6950) fine. Also a slower card with more memory, so ive read, wont offset the performance difference except at the higher resolutions.
I personally have a 6850 and I am able to play bf3 on high on my 46 inch samsung. I am a graphics freak and it looks perfect. I personally think he would be fine with a 1gb 6870 and would be able to run bf3 on high easily. The question is does he want to eventually do a eyefinity setup? If yes then i would go with the 2gb if your only going with one monitor then you only are gonna need the 1gb card.