Is there a metric for the similarity of two image filters?
The &lsquo;k-translation correlation&rsquo; is probably a good candidate for what you are looking for. It measures the maximum correlation between a pair of two filters $\mathbf{W_i}$ and $\mathbf{W_j}$ achieved by translating one filter up to k steps along any spatial dimension and then selecting the maximum thereof:

$$\rho_k(\mathbf{W_i,W_j})=\max_{(x,y)\in \{-k,...,k\}^2\setminus(0,0)} \frac{\langle\mathbf{W_i}, T(\mathbf{W_j}, x,y)\rangle_f}{\left \|  \mathbf{W_i}\right \|_2 \left \|  \mathbf{W_j}\right \|_2}\,,$$

where $T(\cdot, x,y)$ refers to the translation of its first operand by $(x,y)$ and $\langle\cdot,\cdot\rangle_f$ denotes the flattened inner product of the two filters (the second of which is translated). Note that both filters are reshaped to column vectors to perform the inner product. For more details refer to Doubly Convolutional Networks (Zhai, Cheng, Lu, Zhang, in Proceedings of 30th Conference on Neural Information Processing Systems (NIPS 2016)).