i have this gpu (sapphire 7970 6gb) and i play on 3x 1920x1080 , i play mostly bf3
i have 1090t 6core as the cpu , 3cores at 80% en 3cores at 60% during 64player MP bf3 so the 7970 is the bottleneck - it was on 99% - even on my weaker cpu as yours , but it runs smooth as hell in 64player MP , no need for crossfire at least not in bf3
battlefield 4 beta was a whole other story there 6cores all at 95% , but there was an update of the beta after that it was 6cores at 80% , and ofcourse the gpu at 100% , but frames where way lower than bf3 it was not smoot at all , but i think it is just the beta , also people say that bf4beta played much better on windows 8 and i played on win7 64bits
bf3 never uses 3gb let alone 6gb , but one commenter above says 6gb is a no go for these 3 monitors , that is bull cause bf4 beta used 3,3gb vram , but that was with everything on ultra AND 4x msaa and that msaa eats vram without it the game used 2,6gb vram
on guru3d you see that crysis 3 on 1 1920x1200 (so a little higher resolution than 1080) can use up to 2,2gb vram , so 3monitors crysis 3 will use about 4,4gb vram - yes i know resolution is x3 and i say vram x2 but that is my experience with 1920x1080 vram usage versus 3x 1920x1080 vram usage it only doubles instead of the 3le vram usage you would expect
i really think at this resolution even an titan would be the bottleneck
i am glad i have the 6gb version , not even 4gb cards would be good for me right now , so the only cards are my 7970 6gb OR a titan 6gb OR the "new" amd 280x which is a rebranded 7970 but so far there are no 6gb versions so it is not ok for now OR as mentioned above 290 and 290x which start with 4gb but rumours say there will be 6 or 8 gb versions of them