Hockey is a game full of traditions and sentimentality, and that also bleeds into its rivalries. At this point, it's only sentimentality that supports the notion that the Battle of Alberta is top rivalry for either the Calgary Flames or the Edmonton Oilers.
For their part, the Flames seem to have more bees in their bonnets for games against the Vancouver Canucks (and for good reason). Since the last time the Flames played meaningful spring hockey against Edmonton in 1991, they've played Vancouver three times in the playoffs and had a memorable line brawl with them in January 2014.