Mainly because of the cohesion of plot, themes and style, which I mentioned above (Things Are Not What They Seem), but also because this book introduces some of the best characters Rowling has written. As Legolas pointed out, the Dementor are perhaps her most original monster, and they are damned scary; and Lupin and Sirius are endearing beyond words (this may just be me). She also explores and introduces the past as positive influence on the future, for the first time (previously it has been all death and despair) and the effect is remarkable. She does not have to draw the characters of Sirius and Lupin, or Snape, in too much detail. All she has to do is set them up together and let them play out.

As far as Young Adult books go, I don't often read them, and the period when I did is so far gone my memory may be faulty, but I remember them as being sad, poorly written excuses for literature on a whole (of course that may just be what my local library labelled young adult -- I suspect it is a very fluid category). At any rate, Prisoner of Azkaban is better than what I remember of it. But then I still feel this one is written for children.

Or rather, it stands the test of something written for older people in that it is well plotted, cohesion of theme &c. &c., but what I observed about the teacher having to be present in the compartment before the dementor could enter, for example, still marks this as written for younger people, unlike the next book.