If both CPUs were available at their MSRP, then the 5600X would be the obvious choice as it’s faster and more efficient, plus it's supported on a wider range of motherboards. But at today’s prices we’d get the 11600K. Actually no, what we’d do is forget both the 5600X and 11600K and just get the outgoing 10600K, or even better the 10600KF.
The Core i5-10600K is $224 and the 10600KF model (no graphics) posing an even more attractive proposition at $200. Those 35% savings could then go into something else, especially if your focus is gaming. If you’re in need of a CPU upgrade today and have a budget between $200 and $300, the Core i5-10600KF is a cracking good CPU for the money.