You won't get Crysis 3 at max settings with above 60 FPS.
On 1920x1080 with very high details and 4x SMAA I got an average of 45 FPS using a GTX 670.
http://www.youtube.com/watch?v=_J1_zPKa-AU - Video of the performance
It would suit you well, I think it's a great GPU. IF you're looking for performance and ONLY performance then a Radeon 7970 is a little bit faster at the same price, though it also has a higher TDP and if you get a reference design, then you won't hear anything over it's noise level.
Radeon 7970:
Pros:
384-bit
3 GB of GDDR5 - Better high resolution gaming
Very overclockable - Overvoltage
Great multi-monitor support
Cons:
TDP 250 watt
Gets really hot if it doesn't have proper cooling
Lacks technologies
Fairly long compared to GTX 670
GTX 670:
Pros:
Boost - Overclocks itself.
Adaptive vsync
Advanced PhysX
TDP 170 watt
Great 3D support (if your screen allows you to)
Short compared to Radeon 7970
Cons:
Limited overclocking - Can't overvoltage
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MIND that some Radeon 7970 has adapted boost.