The Director of The Nightmare Before Christmas, Henry Selick, was asked just this question during a Q&A and finally put the whole mystery to bed.
According to Birth Movies Death, during a recent Q&A sesh at Colorado's Telluride Horror Show film festival, a little girl asked: "Is this a Christmas movie or a Halloween movie?" Henry answered, "Oh boy...It's a Halloween movie."
Just like that, with a simple answer, Henry solved the whole mystery that's been debated for years. He did explain that it's about Halloween because it's about the people of Halloween – and their reaction to Christmas.
Personally, we watch it on both holidays, because why not?