As I mentioned in my previous reply, "
Between the two, the AMD platform would have better upgradability."
That means choosing the AMD Ryzen 5 1500X + RX 570 4GB (440$).
The
Ryzen 5 1500X (3.5GHz-3.7GHz,
4-Core/8-Thread,
Unlocked/Overclockable, only 65W TDP, with decent stock cooler) is
significantly better than the
Intel i3-7100 (3.9GHz,
2-Core/4-Thread,
Locked/Non-OCable, 51W TDP, with mediocre stock cooler).
http://cpu.userbenchmark.com/Compare/Intel-Core-i3-7100-vs-AMD-Ryzen-5-1500X/3891vs3921
Consider also costs for upgrading. With a Ryzen 5 1500X, you can get an affordable B350-chipset AM4-socket motherboard that can be overclocked already. Upgrade path for the Ryzen could be any of the CPUs above it (1600, 1700, 1700X, 1800X) using the same motherboard.
With the Intel i3-7100, which is non-OC'able, it is logically paired with a non-OC'able B250-chipset LGA1151-socket motherboard. Upgrade path is limited to the i5-7xxx or the i7-7700 (non-K CPUs). If you decide in the future to overclock, you'd have to get a Z270-chipset LGA1151-socket motherboard to pair with either an i5-7600K or i7-7700K (which supports OC'ing). Costs would be higher compared to the Ryzen build.
As for the GPU, there is only a marginal difference between the RX 480 and the RX 570 (http://gpu.userbenchmark.com/Compare/AMD-RX-570-vs-AMD-RX-480/3924vs3634).
Thus, the AMD Ryzen 5 1500X + RX 570 4GB (440$) choice.