The texture packs you see for pc aren't 4k, they are high resolution textures. Meaning that up close textures will be clearer and even from a distances things will look sharper whether you are running 1080 or 4k. The textures for the new Halo look fine, not mind blowing but fine. Halo has usually tended to go with a cleaner look for things so its really not that out of place.
4k is different from textures.
You will see difference running at a higher resolution, but it really depends on how big your screen is and how close you are too it.