The 9700k is stronger than the 6700k in IPC, so you'll get more fps possible, higher limit. But cpu usage can and will change between games. A 2 thread game like CSGO will be getting 300+ fps easily from either, so isn't going to make a difference since the fastest gaming monitor is 165Hz. It's also easy on the gpu, my i7-3770K and gtx970 gets 300fps, but I only see 60, 60Hz 1080p monitor. Put that game on 4k, and I'll still get 300fps possible, but the gpu will be limited to about 60fps because of resolution.
My skyrim I get 59/60fps. Not because gpu is limited, but the cpu has to deal with 170+ scripted mods, so is only capable of 60fps, even though vanilla game it gets closer to 180fps. I could pair my i7-3770K with a RTX2080ti and still get just 60fps, the game is cpu bound. Not gpu bound.
You can play CSGO at 4k on an i3 and get the exact same fps on screen as an i9. Gpu limited.
It's not just what you get, it's how it's used.