I supose that "the 7th gen i3" is I3 7100 (of course I3 7300 or I3 7350K are better).
The role of the CPU is more evident when the GPU is more powerful. With a 1080, the CPU is very important, with a GTX 1050 it would be much less. You can use any of the two and even a G4560 with very small differences.
Ryzen 3 1200 has 4 core wo HT and I3 has 2 core w HT. I3 has better IPC and better stock GHz.
In same games Ryzen 3 1200 is slightly better and in others I3 is slightly better. Anyway if you look at reviews on the web remember that they are usually made with very powerful cards like the GTX 1080 and that with the GTX 1050 ti the differences will be much smaller.
Ryzen 3 1200 It can be overcloked with the Z370 or B350 mobo (but not with A320 ones), but not much.
Very important:
Ryzen requires a fast 3000 RAM and preferably special for Ryzen as the flarex. Due to the "infinite fabric" problem, ryzen is very sensitive to the speed of RAM.
I3 7100 requires a 2400 RAM.
Add the CPU cost + RAM cost + mobo cost and go for the cheapest.