Since I am not well versed in the Detroit Falcons' franchise history I am going to talk about the team most adversarial to the Falcons.  This team would be the Regina Elks who hold serve in the Ciarelli Division with a five point lead in the standings.  It doesn't exactly help that Regina tattooed Detroit 6-0 in a game this season (albeit the current season series record is 1-1.)  Five points with half the season left isn't insurmountable but it's seemed to be a difficult barrier to cross over, even with Detroit moving to 2nd over St. Louis.
Speaking of St. Louis, while I don't know the specifics, a lot of the users on the Detroit Locker Room server say it's the team's biggest rivalry and has history to early SHL.  It was succinctly categorized as similar to the rivalry of Calgary/Edmonton in the NHL