If you're looking to play Battlefield 1 in medium to high settings it's not going to cost you a lot this time around. That being said, the competition in the $100 to $150 price range is rather fierce.
Under $100 - GTX 1050 vs RX 460
In the under or around $100 range the choice is between the RX 460 and the GTX 1050.
All things being equal, the GTX 1050 will give you slightly better performance.
Yet, I have found the RX 460, on occasion for as low as $80. So, if you're on a budget, it'll likely be more inexpensive than the GTX 1050.
Both the RX 460 and GTX 1050 are very power efficient with a TDP of 75W.
Battlefield 1 PC Benchmark (gtx 980ti)
We found the GTX 1050 to be the slightly better overclocker as it had a bit more headroom.
Under or Around $150 - RX 470 vs GTX 1050 Ti
In this price range, there are two fantastic cards available; the RX 470 and the GTX 1050 Ti. The AMD RX 470 is the clear winner here in terms of performance. However, there are more options of the NVIDIA GTX 1050 Ti available at a lower price point.
One other thing I want to mention about either one of these processors.
Having tested them with an i3 at one point, I can say that this CPU will bottleneck them. So, if you have an i3, the performance difference will be very minimal.
Ultimately, you'll want go with a CPU GPU combination of an i5 here or at least a Ryzen 5 Quad-core.