I'm curious now how bad a mutton stink is. Never encountered any. Restaurant menus are always lamb chops.
In my experience, it can be pretty distinctly strong, almost musty in a way. But it also feels like the kind of stink that you can get used to, like a stinky cheese.
Oishinbo presents it as unanimously undesirable, but there are cultures around the world that enjoy sheep mutton. I'd keep an open mind. Me personally, I'll go for it when I can, just to get something different from the standard chicken/pork/beef.