Your below min spec. Minimum GPU 7870 Considering the 6950 was released in 2010.
The 6950 should still hold it's own though providing there's adequate driver support, I think AMD recently dropped the driver support of the 6000 series, however I think that was after Fallout 4 released.
The 6950 is also much faster than the 550 Ti, the system requirements appear to be inflated in favour of NVIDIA cards.
I'm tempted to put my 6850 back in my PC to see how it runs Fallout 4.