HD stipend might be $10K more than AD stipend (that's how my district works, at least). Depending on the difference in years, $20K difference wouldn't be uncommon. $30K would be rare. Some districts put the HD on an administrative pay scale, so that might push up to a $30K difference.
HD has to deal with all kinds of emails from the principal, district fine arts people, parents, community, coaches, facilities people, transportation people. He has to make sure the building will have AC over the weekend for rehearsals, the stadium will be available, the auditorium will be reserved, and there will be buses to take the band where they need to go. He's ultimately responsible for the entire band budget (in many places, that's more than his salary). Anything the AD does that causes issues, the HD has to deal with. When band kids have issues that the AD can't handle, the HD has to deal with it. I'm sure I haven't listed all of the administrative nonsense that the HD does on a daily basis. On top of that, he probably has to work a lot more days in the summer than the assistants do.
So yes, there's a big difference. Early in your career, all you have to do is show up and teach. As you advance, you get more responsibility, and therefore more pay. That's pretty much the way things work in any other career, by the way.