Hi there,
I think it would either be a driver issue or something with the video card itself.
At 1920x1080 u should be able to run everything on ultra with Antialising Deferred off and get 60+FPS quite easily. I'm using a 7850 2GB (and an AMD 960T cpu) and can run it on ultra at 1920x1080 and barely ever get below 50FPS
Maybe try to reset your Graphics settings in Catalyst, do a full reinstall of video drivers etc and go from there?
My settings at 5760x1080 are as follows:
and i usually sit between 35-40 FPS, only sometimes dipping below 30.
When you get back to testing BF3 try these settings as a starting point then work up from there, the settings that seem to make the most difference FPS wise is 'Antialising Deferred and Ambient Occlusion(HBAO)' for myself personally using an AMD card.
Also, have you tested out other games?
Best of luck ^_^