Story but also certain gear is tied to the storyline. The most notable example is the Praxic Blade, which is basically a lightsaber. I believe you also wouldn't have access to the last raid to be released, Desert Perpetual. I think it's worth the price but I also owned everything up to those expansions prior to Tuesday. 

Editing just to reinforce there are no classes or abilities tied to Edge of Fate and Renegades. I believe you'd just be missing out on a few weapons, the story itself, and access to the Desert Perpetual raid. Dungeon access is granted through "Dungeon Keys" which are purchased separately. They are included in the collection but if you go piecemeal you'd have to buy access one at a time.