If you play something like PUBG (not properly optimised yet) and want decent settings the 1060 will be dropping below 60 fps at times. Having the extra horsepower of something like a 1070 or above is going to aid in stopping the drops below 60 fps and prevent screen tearing even if playing at 1080p.
Basically if your card is capable of playing at 60+ fps and your monitor is 60hz you're good. If your card only manages 50-60 fps your going to get some bad tearing.