The Intel Core i5-13600KF wins in 10 out of 14 comparable specs, with 1 tie. Its biggest advantage is L2 Cache (1900% better).
Core i7-6700K wins in 3 specs (Max Turbo Power: 50% better).
Recommendation
Choose Core i5-13600KF if you want the best overall performance — especially l2 cache.
Choose Core i7-6700K if max turbo power matters more to you.