This is always told wrong. If you do not have V-sync on, and you have 70 FPS, as an example, with a 60hz screen, you will indeed see 70 FPS, but there will be many partial frames shown. While the monitor updates its image and a new frame comes in, as a result of rendering frames faster than the monitor refresh rate, the monitor will shift to a new frame before it has a chance to display the whole image.
The frame is shown, just not a complete frame. A 60hz monitor can only show 60 complete frames, but if you have 70 FPS, you'll end up seeing 70 frames at an average of 60/70 of each of those frames.
At 120 FPS, you'll see 120 half frames on average.
Obviously a 120hz monitor is better.
NOTE: if you do not use V-sync, no matter...