A darker world and less talkative bosses
The transition to isometric 3D for Diablo III came at the cost of the dull, dark and gothic art direction of the first two games. The abandonment of the light system also helped to reduce the oppressive part that made their charm.
Gameplay excerpts and trailers indicate that Diablo IV is trying to remedy this, for example with less light spell efforts and duller colors, among other things, but it's not an easy task. Some people don't seem convinced that this is enough to do justice to the atmosphere of the series.
One of the strengths of the first two Diablo titles is that they take the bosses by surprise. From the butcher, to Diablo himself, to Duriel, their presence is sudden and violent, usually accompanied by a single memorable phrase like "Fresh meat" or "Looking for Baal?"
They don't try to instigate dialogue or tell you about their lives.
Diablo III went in the opposite direction, and many demons seem to possess a demonic walkie-talkie so they can socialize with you.
The worst in this area is Azmodan, supposedly a genius general, but who reveals all his plans. Diablo, on the verge of destroying the High Heights, keeps telling you over and over again that it's too late and you'll never get past the next obstacle he's left in your path (even when you inevitably get past the previous ones).
Reaper of Souls has tried to do things differently, but it's not very credible either to pick up each boss' diary in ten segments in the area. Sticking the lore right into the players' faces is counterproductive, and besides the lack of subtlety, it can only irritate those who aren't interested and those who prefer a deeper, more coherent universe.
A more appropriate way to approach this would be to use NPC dialogue as well as Cain's many writings — things that seem to be present in Diablo IV based on the gameplay excerpts and the demo — although we don't yet know exactly how much of that is present.
It's very easy to build up a solid idea of the future bosses' personalities and actions without having to talk to them. Their goals, as well as those of the heroes we play, are too antagonistic to waste their spit on communicating all the time.
It might be interesting to get the player to find out about their next opponent in advance to counter their abilities, or to anticipate their actions on a large scale, and that would be a real possibility in a single-player RPG.
However, with the multiplayer and action orientation of Diablo IV, that would be a lot to ask for. A good story for Diablo IV would also be a good thing, as Diablo III didn't really convince us with its Nephalems and Tyrael's setbacks. We're counting on you Lilith!