It's overkill even if the Sims 3 way playable across three 1920x1080 monitors.
I would actually Google around on how to limit rendering in the Sim 3. From what I have read, even though the FPS is capped at 30 FPS within the game, the Sims 3 allows the GPU to render as many frames as possible. That means if the Radeon HD 6970 is actually powerful enough to render 100 FPS, there is no point in doing so because the Sims 3 is only going to display 30 of them. I recall some poster mentioning a way to limit how many FPS the GPU will render so that the GPU is not running at 100%, generating a lot of heat and using a lot of power all for nothing.