Two points:
1) I checked pricing and the i5-7500 was only about $20USD cheaper ($190 and $210USD). Same iGPU. When I checked max CPU processing the i5-7600 is about 8% faster.
I had to estimate Turbo under load but it's probably 200MHz below Turbo Max thus the ratio should be (4.1-0.2)/(3.8-0.2)x100% = 8.3%
If you had spent say $600 for the PC that $20 is about 3% of the cost, so whatever. Frankly, it's pretty insignificant even for a budget build so I'd probably get the i5-7600 if I was deciding between these two only.
2. RYZEN
If I was building a budget gaming or office build I'd go with Ryzen likely.
The R5-1600 is $200 but has six cores, twelve threads total (6C/12T) whereas the i5's are 4C/4T. The R5-1600 is a far, far better choice and since the Intel CPU's can't overclock AFAIK they should be roughly SIMILAR per core, just with less cores/threads.
*Note that RYZEN benchmarks change as the BIOS situation improves, AND we've seen that future games will optimize towards Ryzen better as Tomb Raider (the last) and AotS both got big boosts from code modified to use the CPU's better.
If anybody cares, the only cost difference I can think of really is that you need better DDR4 memory. Ideally you want 3200MHz (Dual Channel i.e 2x8GB) but I watched a video that showed that most gaming situations with GTX1060 or lower didn't benefit much beyond 2666MHz (and you can likely overclock 2666MHz higher if need be).
You might think that HIGHER RESOLUTIONS are more GPU bound so why would a GTX1080Ti for example want 3200MHz on the CPU when the CPU shouldn't be the bottleneck?
Well, the answer is that the CPU becomes the bottleneck with the slower DDR4 memory. Whenever you get a better GPU you still need the CPU to keep up. It STILL has to send more draw calls to a better GPU so thus still needs faster memory to keep up with it. (and of course there are OTHER situations where you'd want DDR4 memory to be faster than 2666MHz, but it comes down to the COST which may be a lot more for 3200MHz and whether you do anything that benefits from the faster memory)
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