(Besides appearances) I have heard of there being different movesets for them both, but I'm not sure. So my question is: do they each have different stats and moves, and if so could you list the different moves between them both?
They do have different movepools, the male Meowstic being the one with a more supportive movepool, while the female has a more offensive movepool.
Look at the Meowstic Pokedex moves for the moves.