The monitor refreshes the "pictures" 60 times in a second (not exactly how it works but just to keep it simple), and in 30 fps the screen refreshes the pictures 30 times in a second, wich means that the monitor, due to it's lower refresh rate, reacts to the actions from the game slower.
So obviously it's not the game that is reacting to the actions slower, but the monitor you are looking at will infact react slower due to the games 30fps cap.
Furthermore, the monitor would not take longer to react to the action of the game as you put it. Fps makes no odds to how fast a game runs as long as the fps is running at its intended rate. A 30 fps game plays no slower than one at 60, you just miss out some frames that you'd of seen otherwise.
As I understand it its now up to the game what frame rate it plays at. Fifa 14 played at 60 on the new gen so it's safe to assume 15 does as well. Actually only just read what OP wrote beneath the title. Frame rate wouldn't account for the game "feeling sluggish". A low frame rate doesn't mean the game is playing any slower.
Its not even 60fps on Peasantboxes? Wtf? FIFA does not even look good. fut16coin runs it on 2560x1440 and my GPU does not even goes on Max-Clock.