Does it make difference to play at 1080p 120hz?

I have read a lot on the internet and the opinions are mixed. Some say when the game is 60fps 60hz is better, other say 120hz is smoother even if the game is 60fps.Some even say 120hz makes it worse when the game is 60fps. I personally played with it so much I am not sure any more.
Do you play better at 1080p 120hz then on 4k 60hz when the game is 60fps? I would appreciate someone from 343 tech support to answer my question with good explanation.
Maybe on a 1080p monitor it makes a difference but on a 4k TV it doesn’t( 4k that also supports 1080p 120hz).

The hz stands for the refresh rate on your monitor/TV. Faster is better. 60hz is usually what a standard monitor runs. 120hz is usually the standard on TV’s now unless you buy a cheapie. 60hz is the minimum refresh rate you want. When you go below 60hz the screen is not redrawing fast enough to prevent you from getting a headache or red burning eyes… lol

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