These two modernist writers are both famous for the way that they use stream of consciousness in their works to record the ongoing thoughts and feelings of their characters as they develop at the moment of experiencing them. Yet, if we look more closely at their work, we can see that there are some significant differences in their literature. The biggest difference comes through two defining features of their different style. Joyce's work uses what he called epiphanies, and Woolf used what she refered to as a "moment of importance."
For Joyce, his fiction is marked by moments of intense realisation when his characters suddenly discover truths about themselves and are given moments of intense insight. For example, in "Araby," the teenage protagonist, having developed and nurtured his love for the shapless Mangan's sister, is suddenly forced to realise the shallowness of his love and how stupid he has been:
Gazing up into the darkness I saw myself as a creature driven and derided by vanity; and my eyes burned with anguish and anger.
This is typical of the kind of epiphanies that Joyce uses when his characters suddenly are made to realise central truths about themselves and their lives.
For Woolf, on the other hand, her fiction features "moments of importance," which she defined as follows:
Examine for a moment an ordinary mind on ordinary day. The mind receives myriad impressions-trivial, fantastic, evanescent, or engraved with the sharpness of steel. From all sides they came, an incessant shower of innumerable atoms; and as they fall, as they shape themselves into the life of Monday or Tuesday, the accent falls differently from an old: the moment of importance came not here but there...
The "moment of importance" is to record these "atoms" as they fall and thus make up the raw bones of her characters' day. Such moments of importance serve to flesh out characters and allow her to present them as psychologically complex individuals.