Good metric for qualitatively comparing image patches
To start with, 2 images and 3 measurements are not exactly enough to ascertain any kind of statistical model which in terms can be used to define the optimal comparison metric. 

I think you could start to have a look at texture recognition papers for methods and clues. It is an active field.

For what it is worth, I ran a couple of perceptual hashing functions (DCT and Random Projection based) tests and did a little trial with the so called SIFT descriptor. These functions can separate inter and intra class distances, although from 3 images it is impossible to conclude anything.

Code on github.