Mists of Pandaria saw the Alliance and, well, particularly the Horde at their worst - endlessly bursting into conflict, destroying the peace of the land, and escalating small local conflicts (specifically the Hozen and Jinyu in Jade Forest) into much larger and deadlier conflicts.
By contrast, Warlords of Draenor saw both factions at their best. Ignoring Ashran (which was really just an excuse for PvP,) the two factions cooperated just fine in the attack on the Dark Portal and spent the expansion either staying out of each others' ways (setting up garrisons on opposite sides of the continent) or again, cooperating (such as in the battle at Shattrath.)
While I'd attribute the swift success against the Iron Horde partially to the fact that the Iron Horde thought it had an advantage when it didn't (oh, you have modern technology? From our world and time period? That we invented? Yeah, we'll never see that coming,) you could also chalk it up to the Alliance and Horde both focusing their efforts on taking down a common foe. (You can also attribute it to Blizzard's ill-advised "expansion a year" goal, but that's getting a little too meta.)
But in Legion, the factions are kind of there and kind of not.
Val'sharah has plenty of stuff for two major Alliance leaders to do, but Malfurion has always been one of the most Horde-tolerant Alliance leaders (to the extent that a lot of Night Elves decided he was a traitor) and while Tyrande is not as tolerant as her husband, the story of Val'sharah is far less about factions fighting factions than protecting the world from what is sort of the fantasy equivalent of an environmental disaster, along with a personal story of an ancient grudge. So Tyrande is not happy about Horde players wandering the forest, but she's also perfectly willing to accept their help in order to rescue Malfurion and salvage the absolute catastrophe going on there.
The only place in Legion where we've seen a clear faction conflict is in Stormheim, and in fact, this conflict is really the zone's B-plot.
Alliance players are sent there with two goals - to secure the Aegis of Aggramar, sure, but also to attack Sylvanas. Genn Greymane is leading this mission, and not only was he the last friend Varian talked to before he died - an event that the Alliance has no way of knowing wasn't simply Sylvanas betraying them and leaving them to the Legion - but he also, of course, has a history of hating Sylvanas for some pretty legitimate reasons.
Horde players are actually kind of left in the dark about what Sylvanas' intentions were. Having done the zone on an Alliance character first, I was actually pretty disappointed that Horde players really don't know anything more about Sylvanas' deal with Helya and what she was trying to get out of Eyir.
Ultimately, Stormheim winds up as a win for the Alliance, as Genn manages to stop Sylvanas from achieving what she had hoped to do, which was presumably to enslave Eyir and force her to provide the Forsaken with an endless supply of Val'kyr so there could always be new Forsaken.
Genn didn't kill Sylvanas, though she nearly killed him. Still, it counts as a win for the Alliance given that the Alliance only had the simple goal of making sure that Sylvanas failed.
Genn is a king, and has his own kingdom of people (in exile - actually the state of Gilneas right now is kind of ambiguous, though if we treat the Battle for Gilneas battleground as canon, it's still subject to ongoing conflict.) But Genn certainly does not represent the Alliance as a whole. One gets the sense that Genn is operating mostly within the parameters of the mission given by Anduin (we still don't know if he's officially High King at this point, but given that Stormwind is clearly the most powerful faction within the Alliance, that might be a moot issue.) Sure, his attack on Sylvanas' ships is not exactly what you'd call "the situation demanding it," but one doubts that many within the Alliance are going to be opposed to an attack on Sylvanas (though the loss of the Skyfire stings a bit.)
The situation is a bit more complicated with Sylvanas. She is Warchief now - not just a leader of the Forsaken, but the entire Horde. That was a hell of a dicey move by Vol'jin, given how poorly things turned out when his predecessor's predecessor chose his predecessor.
Sylvanas operates almost entirely independently - you travel to Stormheim with her, but she very quickly goes off to do her own thing while her second-in-command, Nathanos Blightcaller (who for some reason now has a Human Death Knight model instead of a standard Undead model like he used to) is the one you interact with more. (While I don't know if undead still feel physical attraction, it wouldn't surprise me if, perhaps in life, Sylvanas and Nathanos were a bit more than mentor and protege, given how they interact in Legion. Also, it would mean that the Windrunner sisters are all really into humans.)
Other than the player character, the Stormheim operation is entirely a Forsaken one (and including the player if you're Undead.) Now obviously Sylvanas is more accustomed to having her own people work for her (the Forsaken, at least until Sylvanas became Warchief, were the most independent sub-faction of all the playable races,) but I've got to say it doesn't really reflect well on her as Warchief that she went off and focused on this personal mission while she's presumably supposed to be coordinating the Horde's ongoing efforts to fight off the Legion.
The real question I have, then, is what exactly the role that the Alliance and Horde factions are going to play in Legion as things go on. It's possible that they're not going to do much - Blizzard said that one of the motivations for the various class orders to mobilize is that while the major factions get distracted in both defending their own lands and fighting each other, someone has got to step up and bear the burden.
It's a bit like how the campaign against Arthas was certainly supported by the Alliance and Horde, but the Argent Crusade and the Knights of the Ebon Blade were really the ones who ensured the victory. Indeed, the former has rebranded back to the old Knights of the Silver Hand while the Ebon Blade is also back on the scene, along with ten other factions (actually, we really can't ignore the Kirin Tor's role in Northrend, even if they were maybe more focused on Malygos - and they're back too!)
Right now, having finished the quests in Stormheim, the only place where the factions pop up (again, ignoring the "all are welcome" druids in Val'sharah) is in the various little PvP world quest areas.
Still, we've got a lot of expansion to go through, if Blizzard is to be believed, and in fact, with the Nightfallen story getting wrapped up in 7.1 and the eventual (they say early 2017) release of the Nighthold raid, and with Helya and Odyn wrapped up in Trial of Valor, there's not actually that many loose ends left in the Broken Isles before we need to head to the Tomb of Sargeras.
Curveballs happen, of course, like the Zandalari in 4.1 (particularly shocking given that there were friendly Zandalari NPCs in the Stranglethron Vale quests that came with 4.0 that were all about stopping the people that their faction would later support in the very next patch.) But I wonder if perhaps the story of Genn vs Sylvanas is not over yet - perhaps we've only seen round one.
I'm not saying we need to focus everything on the faction conflict, though. In fact, it's actually nice to think of this as being one sub-faction versus another sub-faction while most people on both sides want to set aside their animosity to focus on stopping the Legion. But it's complicated by the fact that one of the so-called sub-faction leaders is also the leader of the entire Horde. So we'll see.
For now, I'm pretty happy about helping the Nightfallen resistance, and I'm very eager to see what comes next in 7.1 (I just got Good Suramaritarian, which also gave me Loremaster of the Broken Isles, which in turn gave me Broken Isles Pathfinder Part One. So I'm ready to get to the next chapter.)