His attention to detail and his observational eye. He has a knack for making mundane things (like picking vegetables in Totoro or making noodles in Ponyo) look interesting. Much of that is due to his skill as a visual storyteller.
His characters don't TELL you what they're doing, they show you.
There have been a nuraber of times I've been drawn in by a character doing some routine chore, like baking a bread, frying an egg, or making soup, and I was wondering, "Hmm, what are they doing now? Ohhhh...he's making an omelet." One good example is in Princess Mononoke. There's this one scene where Ashitaka is unconscious and injured, and San gets a slab of meat and puts it in her mouth. She chews it very, very deliberately, and then delivers it mouth-to-mouth to Ashitaka. The whole scene is dialogue-free but it says a lot about San's animalistic nature, the logic of chewing food for someone who must be fed but is "out of it", and the scene even manages to be slightly erotic. It's moments like that that keep me coming back to Miyazaki even when some of his plots turn into garble.
In the hanRAB of most other animators, anime or western or otherwise, they'll have a character tell you what they're going to do ("Anybody want fried eggs?" "HMMM I'd better chew this so that Ashitaka can EAT IT!"), and then they do it. Miyazaki's characters will often do something first and then tell you afterward (if they even tell you what they're doing at all).
Details like these really draw you into the story.
