Rexper :
Go with the Ryzen 1700. Both CPUs can perform 60 FPS in the majority of games, so when gaming they perform noticeably equal. Though the 1700 is just a much better CPU overall with the faster multi core speed.
The 7700k literally makes no sense buying unless you plan to do something other than gaming that benefits from high IPC rather than multi core speed. It only distinguishable performs better whilst gaming when using a monitor refresh rate above 120hz.
I suggest making room for an SSD there. Possibly going with the R5 1600, and downgrading motherboard a tad.
Also, I case anyone was wondering, resolution has zero influence on the performance of a CPU, vice versa. 60FPS at 720p is the same amount of work the CPU deals with compared to 60fps at 4K.
He doesn't say anywhere what resolution he wants. It is almost implied that he would want higher then 60Hz when he puts a 1080ti on each build, unless 4K. If he decides to do 2k-4k gaming above 120Hz then where does go now? He has to completely get a new build if he goes the AMD route as you said, "It only distinguishable performs better whilst gaming when using a monitor refresh rate above 120Hz." Why would you not want to spend a few more dollars to ensure that you will be getting 144Hz on all the newer monitors. I would agree with what you said but unless he posts what resolution and Hz he wants to play at, the Intel build would be the safer build to ensure the higher specs.
(He's also not using the 7700k unless he grabbed my idea that I threw at him but his build didn't change so I assume he's still going to rock the 6700k.)