6950 or 560 Ti. It really depends on your taste (ATI vs NVIDIA), memory wise 2gb vs. 1 gb is more future proof. It is correct that 2 GB would currently come into play when you are running resolutions in excess of 1080p (HD), which is the case in multiple monitor setup. Right now because of this 6950 can give display to 3 monitors at a time, has switchable dual bios (even if one bios gets corrupted you can switch to second one instantly), 6950 can be unlocked to 6970 (not the option in new ones, i guess you have to find older model). All these options are non-existent in case of 560. However, budget wise 560 is much much better as it is inexpensive. Overclocked 560 would reach near the value of stock 6950 in performance and in price too! In the end 6950 is more future proof as games would undoubtedly be made which would require that additional vram, but who sticks around with a card for 3 years? very few indeed.
Tail piece: 6950 is huge and would required a mid tower casing at least, plus its heavy so you have to take that in account too. The choice is yours.