I'd say, Fozzie is closer to Kermit in the Muppet Show and earlier movies (well, GMC not included as I haven't seen it to judge). They're really close, they're the best of buddies. But then, later on, it seems that Fozzie almost gets shafted for Miss Piggy. She takes the place of Kermit's sidekick, if you will. I'll use examples with the movies i know the best.
For example:
TMM: Kermit and Fozzie hit the road, Piggy becomes a sidekick following them to stardom.
MTM: All the Muppets go to get famous. We see how close Fozzie and Kermit are (with saying goodbye, etc) but ultimately it ends with Kermit and Piggy getting married
TMI: Fozzie is the comic relief, and again Kermit and Piggy pretty much get together by the end of the movie. Fozzie has pretty much no relationship with Kermit.