Since you don't play at 4k, unlike the op, your recommendation will change. I assumed you wanted 4k, my apologies.
For your game choices, price point, power availability, and playing at 1080p,
https://www.newegg.com/Product/Produ...-037-_-Product
a 1060 @3gb should be more than sufficient. Its about as strong as the 570 but is nearly 50$ cheaper. Nvidia cards are also typically less of a power hog.
http://gpu.userbenchmark.com/Compare...570/3646vs3924
http://gpu.userbenchmark.com/Compare...-Ti/3646vs3649 (a comparison of the 1060 to the 1050ti your 30$ is very well spent upgrading to the 1060 a 70% boost for a ~25% boost in cost)
Your choice will come down to preference. On a side note, going GPU to GPU of the same engineering (nvidia/amd) is almost always a smoother installation process than switching teams.
If you're looking to reduce your replacement rate on your gpu, try to save an extra 150 and go for the 1070. I realize that may not be possible but really is the best course of action.