That's weird TP, I'm running GTAV on one R9 290, which isn't that far ahead of a 7970, on 5760x1080 with a solid 60fps. All settings high with some on very high but only FXAA and tessellation set to normal. I have the advanced graphics turned off except for the distance setting, which is about three quarters.
Maybe it's a driver thing? AMDs newest drivers still kinda suck, CrossFire still isn't working for me. A bt disappointing, because i could probably be maxing it (without MSAA ofc) if both cards didn't cause the game to stutter.
I also heard the active music scan thing was causing some peoples games to stutter, maybe look into that?