Just found this comparison: http://www.guru3d.com/articles_pages/crysis_3_graphics_performance_review_benchmark,1.html

Yesterday, I ordered a 7850, 40 FPS at High settings + FXAA is more than I expected Can't wait to receive it!

40 FPS with 7850? O.O I have 7970 Ghz edition and i can get about that much (35-40 FPS) with high settings :S

tbh, i was expecting to be able to pull off 60 FPS at high settings with 1920x1080 res. But nope. It's playable but feels really laggy.

40 FPS with 7850? O.O I have 7970 Ghz edition and i can get about that much (35-40 FPS) with high settings :S.
You know, benchmarks are only a way to compare different hardware, maybe they used a scene that wasn't particularly intensive. From other's experience, I expect the 7850 to have playable framerates at Medium + some AA, more than at High, but we will see.

No one should use FXAA in Crysis 3 EVER, when you have SMAA 1x and 2x
Both have similar performance hit to fxaa but much better image quality and no blur.