It depends what you mean when you say it buffers. If it’s transcoding then one issue is that the LG TV client doesn’t support the video and it’s trying to convert on the fly. If it is, then it isn’t a bandwidth issue.
It’s debatable whether the WiFi on the Apple TV is faster than the LG TV. But it should direct play nearly all videos, and moreso if you use Infuse player (paid app/subdcription).
As a person who has used both extensively:
The Shield is better at sideloading. So if you use apps like smart tube next, or other apps like cinema HD, Bee TV to tap into torrent streaming, Kodi for its addons, or real debrid streaming, then Shield is the way to go. It’s got better support for those types of apps.
I’m a heavy Plex user but use the Apple TV 4K (latest gen). Both are great for Plex but if you have a home theatre setup, the Shield is better because of its TrueHD capability.
The Apple TV has a faster UI. Shield is fine but it can definitely lag in places and my Shield is prone to crashing from time to time. Mic on the Siri Remote is the best I’ve seen on a remote. The Google Assistant has never worked consistently for me.
If you’re in the Apple ecosystem, the ATV4k has nice support for Apple AirPods which integrate very well.