I just checked some benchmarks fron my favorite review site and they are showing identical performance in RDR2, 1080p, medium settings (for CPU bottleneck), with 195.9 for the i9 13900K vs 194.3 fps for the i7 13700K.
But in the slowest 99 percentile frametime (lower is better), the i7 13700K scores a bit better with 7.7 ms vs 7.9 ms for the i9.
So yes, the i7 is cheaper, better at gaming and consumes less energy (thus cheaper in long run and quieter).
@Poneybirds is right!
About GPUs: I have been very active on the GPU market recently and have in the past 3,5 years used GTX 1080, RX 6800 XT, RX 6900 XT for a few weeks and am now using an RTX 3080. Mainly because it is a quieter cooler (ASUS TUF) than the 6900 XT (Red Devil) that I bought just before and because of the sudden discount. The 6900 XT did outperform the Nvidia in DCS and is a better fit for Linux dual boot that I am running now. But the fans on the Red Devil were terribly loud. Not AMD’s fault.
It is important to focus not just on the brand name but on the way these cards achieve their similar performance numbers, as it can matter depending on whether you use VR or high pixel count (4K with AA) or on the other hand, if you prefer a cool and quiet operation of your gaming rig.
Last gen (RTX 3000 vs RX 6000), AMD had much more power efficient cards that were comparatively better at lower pixel counts, and suffered a bit towards the high end of high-res VR.
This gen (RTX 4000 vs RX 7000), it is exactly the other way around: now Nvidia is relying more on VRAM cache and has less raw bandwidth, thus saving A LOT on power and creating the most efficient cards ever, while AMD has more raw bandwidth this time and is not coming close to the efficiency (energy per frame) that Nvidia is getting. However, in high pixel count scenarios, such as high res VR, you can be sure that an RX 7900 XT will beat the RTX 4070 Ti.
About VR: AMD had a bug in their drivers for the 7900 series that caused bad performance in VR but that has been fixed in the early July driver update. Confirmed by independent reviewers.
And yes, this does tempt me to buy an RX 7900 XT but I should not, as the incremental improvement over the 3080 is too small to justify throwing away another expected €300 in value in the next year.