Like most others it seems, I'm having performance issues with Rome 2. My machine easily meets the recommended requirements but when it comes down to city battles, the game lags. What's surprising, is that my FPS doesnt go down, the camera moves around quite smoothly, but all units seem to act like the FPS drops. I couldn't work out whether its my machine or the game... if it is the game, I hope they'll fix it.
I've got an ATI HD5900 1gb graphics card which 3 years ago was the top of the range, and even though it isn't any more, it still runs very well.
I was also having issues with textures, I've solved that problem by running the game in a windowed mode. If you are having the same issue, I'd recommend you to try it. You may find that the game isn't cetered on your screen originally, but if you select a different resolution - accept it and then return to your desired resolution, it should fix it. You won't even know you are running in windowed mode.