I don't follow that logic at all. Why does it not make a difference? Lowering the res will give you better fps.
The FPS you get will be limited by your slowest part. More often than not, for gaming, that is going to be your GPU or CPU.
Let's say you want to play SlowSpyder RPG (awesome game btw). At 1080P your current video card can render at 60FPS, your CPU is powerful enough to run the game at 90FPS. You'll still only see 60FPS because your weakest part, your video card, cannot do better.
Now let's say you get a new video card that is roughly 2x as fast, it is powerful enough to render at that same resolution at 120FPS, but you still have the same CPU, it will limit you to 90FPS with that new video card. Even if you lower resolution to make life easier on the video card, because your CPU is giving you all it can at 90FPS, you will not see frame rate increase as resolution is lowered.
In this case the OP's CPU isn't all that fast, so whether he went with a GTX560 or 580 he likely won't see much difference in FPS as his CPU will always limit him. And if he had that 580 and was to lower resolution, well, his CPU is already the limiting factor.