Well, judging by the previous mascots of earlier generations, I believe the typings would obviously oppose each other. If not the typings, then by physiology. For example:
Gen. II: Lugia wasn't a water type, but was capable of learning water-type moves and had access to Hydro pump. According to it's Dex entries, it's habitat is underwater. This rivals Ho-Oh, which is Fire/Flying, and can easily be no match for Lugia.
Gen. III: Ground<Water. The difference can easily be identified thanks to the typings.
Gen. IV: With Dialga being Steel and Palkia being Water, there's a very subtle reference to land and sea, but is basically pointed out as Time and Space. But Dragon=Dragon, so it's a tie anyhow.
Gen. V: Zekrom and Reshiram are obviously weak towards each other thanks to Dragon, but Electric and Fire are rivalled forces, according to Flint and Volkner. I could be wrong, but Dragon=Dragon again. Though Kyurem (which we could reference to "Z") is weak to Fire (Reshiram).
So we could say that, if we had Z along with Xerneas and Yveltal, Z would have a typing weakness to one of those legendaries.
So given the information we already have, Xerneas is obviously land-based and Yveltal is Sky-based. So I'm guessing:
Xerneas: Psychic/Steel
Yveltal: Flying/Fire