I know that a lot of this stuff is familiar to those who play WOW. I don't. So, to me, a lot of this is kind of like "wow".
1) Story. The storyline is just plain more rich in detail and import. Let's face it. In D 2, you chased a bad guy across contrived geography so that you could waste the big bad guys. That's like playing the Japanese army against Gojira. In D III, the end goal is the same, of course. That's what has driven the fantasy narrative since the Epic of Gilgamesh. But the story of how you get to the Final Conflict is so much more interesting.
2) Checkpoints. In D 2, if you died, you resurrected in whatever town you left on your quest from sans any of your goods. You had to restart the game, find your corpse to re-equip your gear and then you had to work your way back to whatever spot got you kilt in the first place. In D III, there are frequent checkpoints, places where you resurrect with all your stuff albeit a tad weaker. No, neither of those is 'realistic', an argument I've actually heard. But the D 2 method is just the grist for grind. The D III method actually advances the game, and enhances how much the player enjoys it.
3) Non-Player Characters. In D 2, you could hire folk to tag along on your missions and 'help you'. Frankly, I found myself spending as much time trying to keep their happy asses alive as I did my own. In D III, you actually get to make decisions about who and what you want tagging along with you. I've already made a few bad ones, but that adds to the game. Not once have I found myself trying to save an NPC before myself.
4) Bad guys. The monsters are much more dynamic in D III. They actually have many levels of difficulty, even among the same critter or tribe of critters.
5) Inferno will break me. In D 2, there really simply wasn't that much to look forward to except a whole lot more grind and simple strategy of leveling up. That Jon tells me I will be broken in D III just tells me that I have something to really look forward to. When i reach it with either character, I might post again then.