The ATV4K will scale down to your TV resolution capability. It might be a tad overkill but buying an ATV4K would future proof your entertainment system, both in terms of TV\Sound System upgrades, and longer support life (ATV4 support will stop before the ATV4K). 4K TV prices are dropping and content is becoming readily available on a lot of services.
4K resolution 4K resolution is 3840 x 2160 pixels, while 1080P is 1920 x 1080 pixels, roughly 2x sharper image. Also, ATV4K supports Dolby Atmos which is a 3D kind of sound immersion. For intense action movies, the room will seem to come alive with sound. But you would also need a sound system capable of Atmos.
In a small room with a large TV, 1080P may look grainy compared to 4K. In a larger room where you view from a greater distance, not as noticeable. The difference might be similar to SD vs HD (480 vs 1080) at a close viewing distance, or 720 vs 1080 at a greater distance. Is 4K essential, no. Is it nice to have, sure. If you are happy with what you have, don't go out of your way to upgrade everything.
Again, be it for video or sound, the ATV4k future proofs your system better than ATV4. The price difference is probably not much on refurbs, but I only see ATV4 on the Apple Refurb store right now. 4K will likely occasionally appear in the refurb store, so you will need to watch for it if you want to go that route.
If your grandkids like gaming, 4K might be a better fit, it has a faster processor. Otherwise, for casual viewing, not a significant difference.