AMD will be more cost effective....and Intel will give you just a bit more on the FPS side especially at 1080p...
If we are talking just CPU, Motherboard and RAM, you can get a i5-8400 6 core CPU which is great for gaming and only a little way away from the 8600K and 16GB of DDR4 3000 RAM and motherboard for $445.75
PCPartPicker part list:
https://pcpartpicker.com/list/hQNR4q
Price breakdown by merchant: https://pcpartpicker.com/list/hQNR4q/by_merchant/
CPU: Intel - Core i5-8400 2.8 GHz 6-Core Processor ($220.88 @ OutletPC)
CPU Cooler: Cooler Master - Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($24.89 @ OutletPC)
Motherboard: MSI - B360-A PRO ATX LGA1151 Motherboard ($69.99 @ B&H)
Memory: Corsair - Vengeance LPX 16 GB (2 x 8 GB) DDR4-3000 Memory ($129.99 @ Amazon)
Total: $445.75
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-11-11 09:18 EST-0500
On Ryzen with an R5 2600 and 16GB RAM and B450 motherboard you are at $354.87
PCPartPicker part list:
https://pcpartpicker.com/list/gHyZzY
Price breakdown by merchant: https://pcpartpicker.com/list/gHyZzY/by_merchant/
CPU: AMD - Ryzen 5 2600 3.4 GHz 6-Core Processor ($159.89 @ OutletPC)
Motherboard: MSI - B450M PRO-M2 Micro ATX AM4 Motherboard ($64.99 @ Amazon)
Memory: Corsair - Vengeance LPX 16 GB (2 x 8 GB) DDR4-3000 Memory ($129.99 @ Amazon)
Total: $354.87
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-11-11 09:13 EST-0500
You can of course save a bit of money dropping the RAM down to 8GB and choosing maybe a cheaper motherboard...
Both options would give a fairly good gaming setup depending on your GPU...Just to re-iterate the 8400 is very good gaming CPU...