Personally, as more of a Nvidia fan, I would personally recommend the Gtx 1060. But both cards are very good cards for a low budget. Both would allow a slight overclock (If wanted) But the Rx 480 is a more power-hungry card, but it is still able to run games at 60+ FPS at high settings.
This is just my opinion, but it depends on you. If you want a card that is less power-hungry, but still performs really well (And does cost a little extra) get the 1060. But if you want a more power-hungry, but a cheaper option and you only lose a little bit of performance, then get the rx 480. If you are on a limited budget, the rx480 can be purchased for under £200, which personally, is a really good deal for the performance of the graphics card. These cards will not be bottlenecked as you have overclocked your processor to 3.8GHz.
So yeah,
GTX 1060:
Added Performance
Less Power Hungry
Costs more (230+/-)
RX480:
Really Small Performance Loss
Costs Less (£180+/-)
More Power Hungry (Maybe louder as it runs at higher temperatures)