Sooooo, the anticipated new abilities for Primal formes have been announced, Kyogre having Sea of Beginnings and Groudon having Land of Endings. They cause Strong Rain and Strong Sunlight respectively, presumably being infinite weather but this is not confirmed.
Groudon's new move is called Cliff's Blade, I'll update this with more info when it is received.
And Kyogre has a move called Origin Wave, which like Groudon's is yet to have details revealed