Should I Choose the i5-6400 or i5-6600K for My Existing PC?

I would avoid spending much on either one and save for a larger platform upgrade instead. A newer, inexpensive Intel system or an AM4 board with a Ryzen 5000 processor would provide a much better long-term upgrade, and you may be able to reuse your DDR4 memory. An i7-6700 or i7-7700 would also be a more meaningful upgrade for your current motherboard because of the extra threads and larger cache.

If you can get them very cheaply, choose the i5-6600K. It is faster than the i5-6400 even without overclocking, and your 450 W supply should have enough wattage for an i5 and GTX 1060. However, because the PSU is generic, its quality is the bigger concern than the rated wattage. Replace it with a reputable model when possible.

Both processors are quite old, but moving from the i3-7100’s two cores and four threads to four physical cores can still help. The 6600K is the better option at the same price, especially if it includes a cooler. Don’t expect modern-game performance to be excellent, though. With a 6 GB GTX 1060, Helldivers 2 may be playable around 30 FPS on low or medium settings, while 60 FPS will likely require low settings and some compromises.

The advertised power figure is not a reason to panic. The 6600K’s higher power rating mainly leaves room for boost behavior and overclocking; it does not automatically draw that much all the time. Still, a generic power supply can fail regardless of whether the total wattage looks sufficient, so monitor temperatures and instability and plan to replace it with a quality unit. Make sure the motherboard BIOS supports the processor before buying.