Yeah 850W is overkill for any single-card setup, even a power-hungry beast like a 480.
I agree with the assessment above that the 560 and 6870 are really quite similar. For BF3, the 560 will have an edge. Both those cards are good 1080p performers right now, though.
It's unfortunate that nvidia hasn't yet released a next-generation card in this price space, while AMD's new cards are either too low in performance (7770) or too high in price (7850). Normally I think of right around $200 as a sweet spot. Of course, the 560 Ti and 6950 are still very good cards, but it'd be nice to have something more efficient there.
If you can possibly scrounge together an extra $60 or so (according to Amazon pricing), the HD 7850 is a significant upgrade. It has a nice performance boost over the 6870/560, serious overclock headroom, and runs very cool and at low power. If you plan on breaking the budget, I'd probably do that rather than a 6950/560 Ti.