I went from an i7-920 to an i7-3770K and gained over 25% improvement in some games with my HD5870 though I shortly upgraded to a GTX680 after that so it's likely 40% improvements would be had.
*The i7-920 is slower than the FX-4300 and I know I get over 40% improvements in some games compared to the FX-4300 though in some like TOMB RAIDER there's minimal advantage.
So it varies, and the better the GPU the more likely the CPU is to be the bottleneck (there's always a bottleneck somewhere).
Comparison:
https://www.cpubenchmark.net/cpu.php?cpu=Intel+Core+i7+920+%40+2.67GHz
and
https://www.cpubenchmark.net/cpu.php?cpu=AMD+FX-4300+Quad-Core
*They look SIMILAR at first glance however the i7-920 is hyperthreaded. Hyperthreading just means the SAME CORE has a separate thread of code waiting to start being processed while the CPU is getting more data from system memory (to avoid sitting idle) however the program must be well optimized to do this (well "threaded" which works in HANDBRAKE to convert video but not as well for games. Most modern games use over TWO CORES but rarely more than three overall but the main limitation (until DX12 comes) is the performance of a SINGLE CORE.
Passmark calls this the "single thread" rating which is a bit misleading for hyperthreaded CPU's but generally with FOUR CORES we can just look at this value to compare CPU gaming performance.
i7-920 single core - 1160
FX-4300 - 1411
i7-4790k - 2530
Summary:
When a modern game runs the "main thread" of code, this runs on a SINGLE CORE (or possibly jumps between cores but either way is limited to the speed of a single core since). When that core hits 100% usage that's known as a BOTTLENECK by the CPU. A comparatively faster GPU would sit waiting for commands at this point. So a slow GPU might be say 80% used and a really fast GPU might be 40% used.
All video games have a MINIMUM CPU requirement that basically equates to running the game on LOWEST settings to achieve 30FPS. If the CPU is too slow you'll never get to 30FPS regardless of whatever else is in your computer.
The MINIMUM hardware for one game might actually be enjoyable but for another game might be unplayable due to massive stutter or whatever.
*Finally, we never know for sure how a game will perform until it comes out though we usually run two important benchmarks:
GPU benchmarks (same high-end CPU with different GPU's), and less often
CPU benchmarks (different CPU's with the same GPU)
So again, some games like TOMB RAIDER have relatively low CPU requirements and an FX-4300 can be comparable to an i7-4790K whereas other games like Fallout 4 will have much higher CPU requirements.