The author of the popular YouTube channel Testing Games answers.
He tested one of the top 12 generation Intel processors with a mid-range 13th generation model. Testing was conducted on a PC with a GeForce RTX 4090 graphics card and 32 GB of RAM.
Results in 1080p below:
Forza Horizon 5 — 255 fps (Intel Core i5-13600K), 251 fps (Intel Core i9-12900K).
CoD Warzon 2.0 — 173 fps (Intel Core i5-13600K), 179 fps (Intel Core i9-12900K).
Hitman 3 — 182 fps (Intel Core i5-13600K), 187 fps (Intel Core i9-12900K).
Red Dead Redemption 2 — 171 fps (Intel Core i5-13600K), 174 fps (Intel Core i9-12900K).
Microsoft Flight Simulator — 155 fps (Intel Core i5-13600K), 144 fps (Intel Core i9-12900K).
Spider-Man Miles Morales — 134 fps (Intel Core i5-13600K), 136 fps (Intel Core i9-12900K).
CYBERPUNK 2077 — 126 fps (Intel Core i5-13600K), 127 fps (Intel Core i9-12900K).
Need for Speed Unbound — 286 fps (Intel Core i5-13600K), 282 fps (Intel Core i9-12900K).
Conclusion – changing 12900K to 13600K does not make sense. Although, if we consider the option of selling the 12900K, then perhaps there is a reason, since the 12900K is significantly more expensive and generally weaker in games. You can change it to 13600K, keeping the difference for yourself.