This is a question with different answers depending on your use case. You can read our page dedicated to explaining the concept of bottlenecking for more generalised info. For now, though' let's get into it.
First of all, it is worth describing how CPUs and GPUs typically work together in a system. You probably know that the graphics card makes sure to render the frames that gets shown on your monitor, and the CPU does... well... a bunch of other things.
In this article we will be referencing the excellent review of the AMD Ryzen 7 9800X3D CPU from TechPowerUp.
Does the CPU matter, or should I spend more money on a GPU?
This really depends. If you want to game very competitive FPS games such as counter strike 2 at the highest FPS possible and have spent a load of money on a 540hz monitor then yes, the CPU matters a great deal since you can easily run into differences in performance of 10-25% between similar priced CPUs. This is because some CPU’s are made to be all-round performers that handles great in many different applications, but are not particularly optimized for say gaming.
If we reference in the testing done at 1080P from techpowerup, you will see that in Counter Strike 2 the 9800X3D CPU scores 573FPS while the intel Core Ultra 285K comes in at 516 FPS (10% lower.) Now, most, if not all, people will not be able to see a difference between such high FPS, but it is still there. In more demanding games such as Cyberpunk 2077 the difference is larger and the core ultra 285K is here 30% slower than the gaming optimized chip.
So we have a clear winner right?
Not really. While there is a clear difference at 1080P, the situation changes drastically if you're using your PC for anything else than gaming at 1080p.
At 1440p the difference in cyberpunk 2077 drops to a measly 1% with 155FPS on the 9800X3D chip and 153.7 on the core ultra 285K.
Going to 4K, the difference still hovers around 1.5%
Why is there such a big difference in 1080P vs 4K FPS?
The answer is quite simple. At 1080P the GPU stops becoming the limiting factor, and the CPU must work incredibly hard to make everything else in the PC communicate together fast enough to utilize all the power the graphics card is capable off. Going to 1440p and 4K means that the graphics card starts to be put to proper work, and games are often limited by how powerful the graphics card is at higher resolutions like this.
In short, if you plan on playing in 1080p at super high frame rates, and have a monitor that can handle refresh rates like that, then you should be focusing on getting a gaming optimized CPU.
If you on the other hand are a more casual gamer, and perhaps even have other use cases for your PC other than just becoming LEM in CS2, then we assume that you also have a monitor that can fit more than a few hitboxes, such as a 1440p 27” or even an ultrawide. In this situation, the CPU matters less and you have a much wider selection to pick from while not sacrificing performance.