It's not as clear cut as you made it.
Sapphire RX 480 is 22% faster at 1080p and 20% faster at 1440p than MSI Gaming GTX1060 in COD: Black Ops 3
https://www.computerbase.de/2016-08...diagramm-call-of-duty-black-ops-iii-1920-1080
https://www.computerbase.de/2016-08...diagramm-call-of-duty-black-ops-iii-2560-1440
BF1 is going to be DX12, which suggests it has a strong chance to be faster on RX 480, just like RX 480 beats 1060 in Hitman, Deus Ex, Doom in next gen APIs. My advice is to not upgrade until October as prices are bound to subside by that time. At the same time, we may see last gen discounts on Fury X and 980Ti (for example $299), as well as rebates/coupons on RX 480/GTX1060/1070 cards. Makes little sense to purchase any card right now for COD or BF1 as those games aren't out for another 2 months.
Right now a lot of $280-300 AIB RX 480s and 1060 are inflated in terms of value. We should see a
$400 GTX1070 drop to $360-370 around November, as is usually the case with the best GPU deals during November.
Make sure to overclock it to 4.0Ghz at minimum.