One of the big pulls for Legion is "class identity." While you might be a boisterous drunken boxer, a faithful adherent to the light or an ominous harbinger of death, WoW mostly works the same way for one person as it does for another. Your class and spec have their own spells and abilities, but the kind of missions you go on are almost always available to everyone else. Calling on a Hunter or a Druid to help clear out some unholy infestation in a sacred forest makes total sense. A Warlock? Well, that's a bit more of a stretch.
Just logistically, I have to imagine Legion's quest experience is going to be mostly the same, though there are going to be a lot of class quests that should make the experience feel a bit more tailored to your character.
It looks like this will extend to non-questing experiences as well.
Legion will of course take place during a massive demonic invasion of Azeroth. Demons are smart and insidious, and so it shouldn't come as a surprise that there are some who are in disguise hanging around Dalaran.
For most players, you'll not really see anything out of the ordinary - just a couple of mages who seem perfectly appropriate to Dalaran's public spaces.
However, Demon Hunters who use Spectral Sight will be able to unveil these guys for what they really are. But Demon Hunters are not the only ones who can unmask these interlopers. Protection Paladins (my main spec!) will get the artifact weapon Truthguard - a shield crafted by the Titan Keepers Archaedas and Tyr that was used to expose Loken's treachery. Truthguard will basically go off when near these demons, giving the paladin an extra action button to reveal the demons for what they really are.
This attention to detail is something that makes me very excited about Legion. Yes, it's important to have good dungeons and raids and a solid progression system, but Legion looks like it's going to be upping the immersion factor. These small details might not mean anything in the grand metagame, but they give life to the world in a way that makes all the big confrontations feel more impactful.
I hope we get other class or spec-specific world detail. For example, I really hope that walking into Scarlet Monastery with the Ashbringer has the effect the old Corrupted Ashbringer had back in the day.