I have it on good authority that off the theatre set where the Muppet Show is and was filmed, Fozzie is bullying, mean, swears a lot and drinks heavily. God knows how he keeps it together and projects a funny cute shy image on the show. Also, he and Kermit can't stand each other in real life. Fact.
On the other hand, Miss Piggy
keeps her diva act strictly for the show, off set she is lovely and charming and genuinely kind and caring. She does a lot of charity work and support and gives most of her money away to animal support and vegetarian projects and charities.