It's very good I used the same monitor with a Nvidia Gtx 780 OC and was able to play Battlefield 1 on medium at 2500p and 120Hz without any problems.

For which application? Gaming? Video editing?
Which resolution, which game and how many FPS do you want to achieve?

The inexpensive Nvidia GTX 1050 Ti manages the 165 HZ without any problems.

I am of the opinion that it does not necessarily make sense. Why invest 700 in such a monitor and then perhaps only use half of it? I have this monitor and own a 1070 and am very satisfied with it. If you want to play games on High or Ultra with the 1060, you won't get 120 FPS depending on the game.
My conclusion: it should be a 1070.