How should I think when I want to compare mu and sigma for different images in VAE?

I'm searching for a way to compare mu and sigma values of the encoder network's output of variational autoencoders.

In detail, imagine I trained my VAE on the MNIST digits dataset using the official training set. Then I choose 1 sample from number 5 and another one is from number 9.

When I feed my numbers -which are chosen randomly, numbers 5 and 9- to the encoder network, the encoder outputs two vectors; mu and sigma.

How should I compare the mu_5 and sigma_5 with mu_9 and sigma_9?

Maybe, I can sample a latent vector z using prior distribution -Normal Dist- then compare latent vectors in terms of for example with MSE. But I'm curious to learn how to compare mu and sigma variables directly?