if an app is also available on another device (like iPhone or Mac) there should be screen shots of the appleTV version. So you can look up apps on the phone to see if there is an aTV version of the app (I'm not sure if this is the case 100% of the time, but should be most)
every app you're using on the LG will have a version on the aTV
the aTV has better navigation, and a bit smoother app experience normally, both due to the aTV's faster processor, and there are more apple end users than LG end users, so it makes more sense for app developers to put more focus on the aTV. The majority of the code can also be shared between aTV, iPhone, and iPad, Yet another reason the version on an apple device will be more polished.
the aTV does have some advantages outside of just the apps.
Depending on which LG you have, having airplay is nice to send a video to the big screen, not the best way for long things, but it does work
if you get some smart home devices, the aTV adds a few features.
-It can work as a home hub, meaning it will act as a go between when you're away from home to allow you to control and monitor your devices from anywhere. Including cameras. (all sizes of HomePods and iPads also do this)
-it will run automations without your phone at home, want the house to look "lived in" when you're out of town, automate lights on and off. You can also have the front yard lights come on at sunset, or as you turn onto your street.
-if you've got a compatible video door bell, the image will appear on your TV screen when the bell is pressed.
-you can view cameras. "siri, show me the backyard"
-the brand new aTV4k has thread. Thread is a new-ish wireless protocol designed for home automation. It's lower power and longer range than bluetooth, and was built from the beginning to be a mesh network, so it's pretty solid. The aTV works as an "edge router" that connects your wifi network, and the thread network. the Homepod mini also has this.