I have a 60hz monitor. But I feel like games could run better either he 1070
Ofcourse, certain games will benefit the beefy GPU, especially if you want high graphics settings. If you have to lower the settings to achieve stable 60FPS - go for it. Other games might feel more snappy with higher frame rate even on 60hz monitor.
But the general downside is that you monitor is unable to show framerates higher than 60, so it really doesn't matter if your pricy new card can output 100FPS.
It still can be your futureproof GPU to play comfortably at 60 FPS for several years.
I would go for 5700XT if I were you, though.