Honestly I think it was both a step forward and a step back. The world of Diablo III felt much more alive, thanks in large part to the wonderful NPCs scattered along its fringe. None of that credit can be passed along to the main story, which even manages to be grating during the cinematics at times. I never got tired of watching Diablo II's cinematics, but I have no interest whatsoever in Diablo III's. They just aren't terribly interesting or surprising, and that's what's missing compared to those moments in Diablo II. God, that moment at the end of the game, when Marius utters the word "Baal" and completely loses his shit...nothing in Diablo III's cutscenes even comes close to that. Not even in the same league.
That said, I think it's important that we don't pile too many accolades on Diablo II. It was disparaged upon release for the "ya just missed him! you suck!" tone to every bit of story which deigned to involve the player, and I think that's still an accurate criticism. Diablo III involves the player in much more meaningful ways...it just doesn't do it very well at all. In fact it does it so horribly that I long for the days of operating quietly behind the scenes and letting the chips in the great cosmic conflict fall where they may.
Lord of Destruction is really the only entry in the series that nailed it. The cutscenes were stellar, with more style than all of the Diablo III cinematics put together. You showed up at the fortress as an important figure, and you interacted with this remarkable group which one of the most popular classes hailed from...awesome!! Finally we see some of that great back story explored, finally we get to see the characters we're actually playing interacting with their own kind, finally we feel like we really have a stake in the conflict. But that was it! Very little exposition is needed. It was there if you wanted it, but as soon as you show up in the fortress you are sucked in. That final cutscene flows perfectly from the moment Baal goes down; it manages to finish the story that began with Marius and Tyreal while still feeling like our story, like the player's story. Neither Diablo II nor Diablo III accomplished this. The original Diablo comes close (ultimately failing by stripping the player of control), but the manner in which the world of Sanctuary was filled out and explored in Act V made for something special.