Fps starts with the cpu. In games that are optimized for 4 cores or less, the 6600 will get more fps, in games that are optimized for 8 threads, the 4770k should be stronger.
There's multiple other factors, npc Ai can be very hard on low thread cpus, so the 4770k is often better on multi-player games or games with lots of npcs in towns etc.
That info goes to the gpu. The gpu is going to try and put all the fps sent to it onto the monitor. The 5700xt is a considerably stronger gpu at 1080p than a gtx960, so if both cpus sent 100fps to the gpus, the 5700xt could do all 100, but will also swing as low as 20, the gtx960 might only show 70, but also swing the low 20fps. This'll look like a spike in fps to the 5700xt, but only because it has greater range.
Whether you get lag spikes has determining factors too, like game optimizations, the gpu drivers, what stuff is sitting in temp files, hdd vs ssd, the Lan drivers, the internet connections, the motherboard nic chipset, windows cleanliness, hdd condition of fragmentation, how much ram the game has to work with, all sorts of things can affect that. Not just the cpu or gpu.