The difference is that Papyrus is actually a good font while Comic Sans has been known to induce seizures. Although it is overused, the
problem with Comic Sans was never overuse (and, in the case of Comic Sans, one use constituted overuse); the problem was that Comic Sans is unbearably ugly. It is not a good font.
I like Papyrus. I've used it from time to time myself.
Wikipedia notes that it is used as the title font for
The Crocodile Hunter and on bottles of Arizona iced tea. The only time the use of Papyrus bothers me is when it is used as a general-purpose font for body text. It is great for titles and special elements, but I saw a church bulletin done completely in Papyrus. It was awful.
Is it really possible to overuse a good font? If so Times New Roman is probably the most overused font in the world.