1080p is far better for the more modern games such as Battlefield 3 and Crysis 2+3 etc. The main reason being there is more detail in the game world, and so a higher resolution means more pixels, meaning more detail on your screen. A lower resolution gives you less pixels, and so less detail.
Think of it as a piece of gridded paper, and you're trying to fill in squares to make a circle. The smaller the grid, (resolution) the less squares (Pixels) there are and so the circle will appear more square and less rounded. But with more squares the circle will appear more rounded and less blocky.