Improvisation, obviously. You can hear if something is improvised, which is something you may think is not really possible. How can you know if you only know the notes? Well, it is of course possible to trick someone. You can memorize some else his improvisation.
You judge improvised music differently from composed music. Composed music needs to be absolutely perfect, whatever that means. Improvised music shows, in a sense, personality. The improviser needs to be 'perfect'. How perfect is what she plays doesn't really matter.
Also, I find it strange people say what they like about jazz is harmony. Because harmony is the no.1 thing in classical music. In Jazz they just string a bunch of chords together and repeat that several times. And in a sense, no matter what the chords actually are, it will do. Just play it the right way and then play the right notes over it and it will be jazz. And the better the improvisers are, the better the jazz.