Well, for all the stories Blizzard's made recently... This has been the best. That said, it's not good. I was sincerely expecting something like "Even Greater Darkness (tm) is coming, we need to ally with our old enemy, Diablo!" as that's been the main story in every single Blizzard game eversince Warcraft III, counting out some of WoW's smaller stories.
Kudos for killing Cain, it was a bold move and overall quite well done, even though the slightly cartoony graphics ruin the moment on the ingame cutscene.
Overall though, the story had a feeling that Act I was made first, then the rest was rushed. Act I's longest, too. It has good moments, less annoying boss-demon-taunting-you monologues (even though there are some, they still fit in). Above all, it still follows clings to Diablo I and II's athmosphere. Tyrael being the Stranger is no surprise, however, and without the echo his voice feels off. Even worse, he doesn't feel like the wise and brave Tyrael we know - he feels like a dumb side npc nobody cares a crap about. You know, the black man in the movies who always gets killed first (no racism intended). This is a huge demystification of the character - almost to a point of ruining him.
Act II is the worst. It feels rushed, story jumps ahead with huge steps and we get introduced to a badly written companion. The good twist is that everyone can guess from the start the boy king is a demon, and it's never blatantly underlined - even better, none of the side or player characters even are like 'oh noes it's a le demon boy king, we have been betrayed'. That does, however, raise the question of how can such a Lesser Evil call himself the Deceiver - after all, he didn't really fool anyone.
Act III picks up again. Arreat, siege, scenery that brings back good memories. It's all well made and good. Except for drawn out "search item a or place b or item c from place d then return them to place x" that include constant hologram of mr. Azmo or his lieutenant making empty taunts. As someone pointed out before, demons in Diablo used to be scary because they only spoke a line or two on demonic voice - right before they charged at you. Long conversations that boost your character's ego by making him/her taunt Lesser Evils no one can kill is simply making the demon lords feel like annoying loot automats.
Act IV: Well, there's the moment where you see Leah die. For me, it felt good - she was a meaningful character in the story and having no one to pass on Cain's teachings anymore feels like a true loss. Moreover, she just dies and it's not needlessly dramatized - except for Tyrael's ridiculous comments, loss of self esteem and overall non-Tyraelish behaviour. If he didn't feel like the archangel from Diablo II through the game, this is where you actually start wishing you could just push him down from a bridge in High Heaven. And then the Heavens themselves...Again, Diablo II had that "I need to go to Hell? Really?" moment before you step through the portal and Diablo III manages to capture the same feeling. At least for the few moments before you realize that yes, this is the capital of angels and yes, they're all petty whiners who are just as bloody annoying as the demons you kill. Then there's Diablo who also finds his voice to constantly tell you how you didn't just ruin all his plans - up to the moment where he dies. This is where it all goes wrong. Angels don't feel like the virtues they represent, demons don't feel terrible, Diablo feels blatantly stupid in his "hey I just ressed myself and now I charge into Heaven with this new female body I have" thing he's got going on. This, more than anything, makes ruin to the feel of Act IV - Heavens in themselves are well represented and visualized, granted you could've just claimed it was angels' most important bastion or somesuch instead of *the* Heaven.
Summarized, the storyline in itself is fairly alright. However, angels and demons being reduced to squabbling punk kids is a huge let down and the way Tyrael is handled in the story I could call sacrilege if I was a huge fan of his. In short, the story's trying too hard to be epic and ends up being ridiculous instead. And saddest part, of course, is that this is the best story Blizzard has created in a while.