Green Bay and Chicago both have championship history and for the most part in the older days would have to fight each other hard en route to a championship, so they are on a bit more equal footing in their rivalry
With Minnesota and Green Bay, Minnesota sees GB as the team that has won all those championships while we've come so close yet so far on seven different occasions (4 SBs, "Hail Mary", 1987 and 1998) and since GB fans love to hang that over our heads in the same way that Yankees loved to hang it over Sox fans before this year ("0-4" = "1918") it is very fierce in the same way