Actually, there are differences other than those outlined.
For one thing, the single core boost of the 8600k is 300mhz higher, at 4.3Ghz rather than 4Ghz.
The all core boost is 300mhz higher, at 4.1Ghz rather than 3.8Ghz.
You might not think 300mhz is very significant, but try running a CPU at 0mhz and then at 300mhz, and see how significant it actually is. An extra 300mhz on six cores can translate into a lot more muscle under demanding conditions.
People spend a great deal of time and money trying to gain an extra 300mhz out of their overclock, and I can promise you that 300mhz CPU clock speed will net you far more of an increase in performance than any attempt at overclocking memory or tightening timings will ever provide. And people go through hair pulling, teeth grinding endeavors trying to do that. So, 300mhz does matter, at least somewhat.
Also, obviously the 8600k can be overclocked, which may net you an extra 300-500mhz (Or more if you're willing to push the envelope. I don't recommend pushing it more than maybe 4.7Ghz for a daily driver, but some folks definitely do it.) resulting in potentially an average estimated gain of about 600-800mhz above what you could ever have with the i5-8400. 600mhz difference on the same architecture can definitely be "felt" and will translate into recognizable performance.
So that alone makes for three good reasons why you might want to choose the 8600k instead.
But if you do go with the 8400, it's not going to "hurt" your performance either. It WILL still pair very well even with a high end card. Just not AS well.