You're not missing much. I have it on my iPad Pro and a true 120hz tv. You can barely tell. And I’m a somewhat of a home theater pain in the ass. It’s just not that noticeable
I’m curious how you arrived at that judgment.
Barely any true 120fps content exists at the moment except for maybe on YouTube. And I can think of only one or two movies filmed at HD 120fps (Billy Lynn and Gemini Man). HDMI 2.1 isn’t on any devices yet for 4K 120fps.
I have a 120Hz TV too. But what you’re seeing right now on your TV is largely frame duplication using 3:2 pull down based on 24fps content. The result is “fake” 120fps, and isn’t indicative of what real 120fps is.
Regarding the iPad Pro, it’s 120Hz but also LCD. LCD doesn’t hold a candle to OLED response times (or micro LED, if we’re talking the future).
Trust the pro-120Hz crowd here. Once people start recording and watching actual 120fps content using 120Hz OLED screens, people will never want to go back to 60Hz (on the iPhone) or LCD (on the iPad).