The Intel Core i5-13600K wins in 9 out of 14 comparable specs, with 1 tie. Its biggest advantage is L2 Cache (1233% better).
Core i5-9600K wins in 4 specs (Max Turbo Power: 48% better).
Recommendation
Choose Core i5-13600K if you want the best overall performance — especially l2 cache.
Choose Core i5-9600K if max turbo power matters more to you.