Higher texture resolution no improvement I am experimenting with some image maps from Andrew Price's Poliigon site, I am comparing two colour images for the diffuse texture, a 1k and a 3k, but I can't see any difference, surely I should get better results with a higher resolution image:

The node setup:



The image texture size - this is for the 3k image:



The render settings:



Output from the 3k image texture:



Output from the 1k image texture:
Higher resolution texture would theoretically improve surface quality for closeups, in the sense that texture might look less blurry.

"Might", because if you are far enough from the mesh surface the difference will probably not be very noticeable and at lower resolutions it becomes harder to see. 
JPEG compression might also wash away some of the detail.

Besides you seem to be using a mix of 1k and 3k images in your node setup, which would further dilute any subtle effect it might have.

My guess is, for your use case and current rendering resolution 1k texture would probably be enough.