ChipFlip
A twelve-core AMD chip for $209.95, or a fourteen-core Intel chip for $220. On paper the used Ryzen 9 7900X and Core i5-13600K look like different classes of processor competing by accident. The core counts are misleading in both directions.
Intel's fourteen cores are not fourteen equal cores
The 13600K runs six performance cores and eight efficiency cores. Those E-cores are real and useful for background load and multithreaded throughput, but they are not equivalent to P-cores, and a chip described as fourteen-core is doing some marketing work with that number.
The 7900X's twelve cores are twelve full Zen 4 cores, all identical, all with SMT. For anything that scales cleanly across threads, rendering, compiling, video encoding, it is the stronger processor and the gap is not subtle.
For gaming alone, they're much closer
Games rarely use twelve full cores. The 13600K's performance cores clock high and its gaming results land within a few percent of the 7900X in most titles, sometimes ahead. If this machine only plays games, the extra AMD cores mostly sit idle.
Platform and power push it back toward AMD
Same story as elsewhere in Intel's 13th and 14th generation lineup: LGA1700 is a finished socket, AM5 is not. The 7900X also runs on DDR5 only, while the 13600K can use DDR4 boards, which is the usual cost escape hatch.
Worth knowing about the 13th and 14th gen Intel parts specifically: those generations had a documented instability problem tied to voltage behavior, addressed through microcode updates. A used 13600K should be on current firmware, and it's worth confirming the seller's board was updated rather than assuming.
Bottom line
The 7900X is the better buy at $10 less, especially if you do any production work or want an upgrade path. Choose the 13600K only for a gaming-only build where you're reusing DDR4, and check the microcode situation before you buy.