Yeah, when it comes to the on-ice stuff between Leafs/Habs, the rivalry doesn't really exist, and never really has in my life-time. Between the Leafs' long stretch in the Western conference, the lack of playoff series, and the tendency of the two franchises to take turns being awful, the "rivalry" is purely a historical thing at this point.
For me, the Leaf/Hab rivalry today mainly comes down to the fact that, out of every 10 hockey fans in Toronto, it seems like at least one or two of them are the most vile creature imaginable: someone who grew up in/lives in Toronto, yet they hate the Maple Leafs and love the Canadiens with equal degrees of passion.
When you have always known a few of those people throughout your life, it does add something to Toronto/Montreal games. Either way, someone's having to put up with some trash talk afterwards.