Only reason I don't own it now is because I traded it for a 1440p 144Hz monitor. I owned this 4k monitor for a few weeks and I miss it. The video quality is awesomeif I could ever watch it I tried playing the videos on my MacBook Pro and there was a lot of lag and choppiness. Then you can turn down settings to 1440p and 1080p for gaming and you'll be able to watch video in 4k. I recently bought a Sony mirrorless camera that records full HD (1080p) at 60p and 4K at 24p. If you can afford it($250-$325), I recommend getting a 4k monitor. It kind of sounds like you may want to set it to 'Display' instead of 'GPU' since you said the switch looks better when outputting to 1080p. I have mine set to that and think it looks better when playing 1080p games, but test it out yourself and see. It won't look as good as 1440p but it will greatly improve FPS because you are in a lower resolution. If it's set to GPU your TV will always be outputting it's native 4k image. Turning down the resolution to 1080p is just that, 1080p. Using these settings will have very minimal impact on your graphics, give you a great deal of extra FPS and it will use much less power and usage on your GPU/CPU.
You can also turn down things like shadows(low to medium), grass quality(medium), hairworks(OFF) and ambient occlusion(always put on low). You can turn down AA in 1440p in the majority of games because with such a high resolution, AA is not necessary.