The myth
Just buy the more expensive CPU and you will get more frames. Every second forum thread hands out this advice, and it sounds reasonable: more money, more performance. It does not work that way.
What is actually true
CPU and graphics card work like two conveyor belts in a row. The CPU prepares every frame, the graphics card draws it. Your game can only show as many frames per second as the slower of the two belts can handle.
If your graphics card already sets the limit, you can double your CPU and gain exactly zero additional frames. That money is not badly invested, it is invested without any effect, which is worse.
The grain of truth
When the CPU really is the brake, a stronger one helps immediately. That happens mostly at high frame rates and low resolutions: the smaller the image and the more frames per second, the more work sits on the CPU and the less on the card. Exactly then, and not otherwise.
What to do instead
First find out which of the two belts is the shorter one in your machine. Only then do you know which part would be an upgrade at all. Everything else is guessing, and guessing is expensive with hardware.
That is what the bottleneck check on this site is for: it compares CPU and graphics card for your resolution and tells you which side is braking, before you spend money.