OK, I played last night for around 4 hours, but that included a lot of fiddling around with graphics options to test performance. I played D2 around 9 months ago on the same machine, so the tech stuff is the same but my memory might not be 100% accurate on how D2 was. But here goes, with some very minor early game spoilers:
First, DKS looks better than D2 for sure. Textures are really nice. Faces look good. After changing settings around the only performance increase I got was with reducing the draw distance, and even then it looks great. Lowering textures didn't seem to change performance.
On my non-awesome system it runs pretty smoothly when exploring and moving around. In the dialog cut scenes where you see the characters talking, it gets really choppy, and strangely, the cursor gets really slow and sluggish. Again, lowering textures didn't seem to help much here either, but it's not a big deal… annoying though when trying to select Mindread or Trade.
In the few melee battles I've done the performance is still choppy and gets confusing because of this. The goblins sometimes seem to "blink" from one spot to another, and their animations aren't much better than I remember them from D2. The combat does seem much easier though, at least the small amount of it I've seen playing on Normal.
Items that are revealed from Mindreading or quest knowledge (example: the key on the rafters, or the key in the kettle) have a big, sparkly glow that I don't remember from D2. It was more subtle then I think. You cannot miss stuff when it's revealed now. However the key took me several minutes of annoyingly trying to reach it. Jumping didn't seem to help... I just had to maneuver into EXACTLY the right spot to grab it. Annoying.
The voices are great. I'm not sure how much they changed here, but I haven't run into any bad voice work yet which is really saying something.
So far I'm really liking it, though I may lower even more graphics settings to see if I can get better frame rate/performance in combat.