I had this problem not long ago, albeit with an i5-6500. I was upset that games like Fallout 4 and Battlefield would plummet a bit in CPU intensive areas (especially cities in F4). I did some research and avoided upgrading to an 8400 by simply getting faster memory.
One of my sticks died in my 16GB dual channel setup @ 2400mhz. The rest of my games ran without issue using the leftover stick but Fallout and Battlefield tanked hard. Borrowed identical memory from a friend and everything shot back up. Simply going from single channel (1 stick) to dual channel (2 matched stocks) without any other tweaks or increases (still 2400mhz) saw gains of 10-15 FPS(!!!). Currently using 1070 Ti that was mostly CPU bound, your results with a 1060 may vary, it’s not CPU bound.
So, I do more research and find there are massive gains in a few games by going with higher RAM speeds. Decided to replace the old 16GB set with a dual channel 3200mhz 8GB set and now Fallout 4 and battlefield never EVER dip below 60FPS and my minimum and average FPS on CPU intensive games jumped by ~20-35 FPS. As you can imagine, this was quite a shock after hearing more ram>faster ram for years. Turns out that’s not the case at all anymore.
—TLDR—
ALWAYS ALWAYS ALWAYS GO DUAL CHANNEL
2133 - Entry level minimum performance
2666 - Absolute sweet spot for price/performance
3200 - Where games stop seeing tangible increases (diminishing returns)
3466+ - Only if 0.05% increase in benchmarks and +1-2FPS past 3200
Going from 8GB to 16GB only give 1-3 FPS boosts, shorter load times by 8-12 seconds, and in some cases (GTA V, 1 or 2 others) dropped FPS by 1 or 2.