4K is 3840 × 2160 pixels, which is better resolution than 1920 x 1080 pixels. That doesn't mean, though, that either is better than the other.
But, that is meaningless if the image is not of high enough quality to be presented on those screens. Example - a 72 dpi image blown up to fit either of those screens will be terribly pixelated.
Would you notice any difference if comparing the same image on both screens?
Perhaps creating a few image files of different sizes/quality and displaying each file on both devices to compare would be most helpful. Most electronics stores should permit a shopper to make such comparisons on their display working models.