For me the advantages are:
1. Doesn't use Java
2. Simpler/Quicker to configure
3. More modern webui (though I recently found a good desktop subsonic client, sonixd which somewhat negates this)
Also, I haven't used the airsonic fork, but I was using subsonic before switching to navidrome
I found subsonic to be rather... unreliable. once in a while the database would randomly become corrupted and I'd have to delete the database files and start over. I haven't had any such problems with navidrome, it's been rock solid.