While I can understand that the Bears/Packers rivalry is stronger than Vikings/Packers, your baseball analogy is much closer to the Vikings rivalry. The Packers have the rich championship history (like NY) while the Vikings have the "so close yet so far" history (like Boston before last year), and of course Packers fans love to remind Vikings fans of this at every opportunity (again, like NY to Boston)
The Packers and Bears both share rich championship history, so they'd be more like... I dunno actually.