The console runs Windows 10, and it's x86. People will tell you a GTX1070 is a much faster GPU because it's a much faster GPU.
Taking an RX480, underclocking it and adding a few cores is not going to magically make it compete with a card which is 50~100% faster in games.
Especially when it's paired with a CPU which is perhaps on par with Piledriver IPC, with half the clocks.
A gtx1070 is just over £400, where you getting a case, motherboard, ram, storage, controller and keeping price parity with the one x?