Here are some things to listen for and keep in mind about Moon's sound...
The raw grooving beats that despite the wild playing stay together and have actual dynamics.
He played large drums with coated heads like Bonham, but used 1-ply heads which gives a distinctly different sound to Bonham's coated heads. Top that off with the fact that he used birch shells as opposed to Bonham's maple which gave him a more cutting sound.
Most of Moon's playing was not in the forefront of the mix. This actually helped convey his wild playing more because you could not hear every single note clearly, but you could tell a lot was going on.
Another notable trait of Moon's playing is his spontaneity while playing and how he offsets the typical rhythms. While it is not always easy to hear because of the mix, listen closely for how he doesn't always really on the typical two and four snare rhythms.