We’re talking Alder+DDR4 and we’d have to take into account current prices for both Alder and Zen3, which would leave us with 5800X vs. 12600KF or 5700/5600X vs. 12400F. When using DDR5, the 12400F matches the 5800X in gaming, so the 12600K would win. When using DDR4 the 12400F is at a major disadvantage, so the 12600KF would have trouble recouping the difference with higher clocks and more cache.
The budget gamer’s landscape today looks as follows:
- Zen3D would be amazing, but it’s dead Jim
- Zen3 is fine but meh
- Alder Lake would be fine(r), but they made it expensive because “availability”
- Arrow Lake would be yummi, but DDR5 is alien acid dripping through wallets
- Zen5 is a bitter reminder you should have upgraded last Christmas
The only path forward I see for the OP is to either hunt a second hand Alder Lake or go with a new AM4 build. If by some miracle they stumble on a cheap 12600K, then go for it. The end result is very similar, if I were the OP I would focus on what motherboard I like more instead.