I can only notice the difference between 120Hz and 60Hz displays if I look for it carefully.
OTOH, I can easily see the strobing of the majority of LED light bulbs, especially in my peripheral vision. LED light bulbs typically pulse at 120Hz (North America, 100Hz mostly elsewhere). I know immediately whether a room is lit with LED light bulbs or incandescent, even if they are the same color temperature, because the LED light is strobing. Peripheral vision is very sensitive to movement (probably for evolutionary reasons), and I perceive the LED strobing as a slight movement shimmering.
Given that, I find it weird that I can barely notice 60Hz display vs 120Hz.