There is no CPU cap, it keeps scaling up at 1080p. In many e-sports games you won't even get better performance beyond a GTX 1080 provided your CPU is fast enough.
There can definitely be a high amount of variation. Games like CSGO or DOTA 2 don't require much as far as GPU a 1070 will pretty much keep you pegged at 300 FPS. StarCraft 2 is a bit headier on the GPU side if you want to up the graphics. I'm curious about a wide variety of games, though. PUBG, Fortnite, RoE, SC2, Black Ops 4, Ark, Path of Exile, Overwatch, Destiny 2, World of Warcraft, Battlefield 3, etc.
I found my 1080 and 1080ti had little difference at 1080p when I upgraded. I then moved on to 120hz low motion blur (ulmb) and while experience wise it feels the same, it started showing an edge at that resolution, albeit not much. I think going by that metric of rasterization games and current CPU performance you are pretty much not going to see an 2080ti RTX edge out a 1080ti by much at all to make a difference.