There are notable differences between the two methods depending on the specific way in which Jung and Freud approach the unconscious life. Here is a brief list:
Subject Vs Object Level
For Jung, the dream is interpreted on the subject level (the elements of the dream are components of the dreamer's psyche - archetypes such as the shadow anima, animus, center) - for
Freud, on the object level, which involves placing the dream in a real or imaginary social setting.
Prospective Vs Retrospective
For Jung, the dream has a prospective character, meaning it points
to the future development of dreamer's actual psychical conflict - for Freud, retrospective, in the sense that it refers to events from the dreamer's past, most often from his/her childhood, that affects the actual life
of the dreamer.
Compensation Vs Repressed Wishes
For Jung, the dream has a compensatory character - for Freud, it is the hallucinatory realization of a repressed wish.
For Freud, analysis leads
to the revelation of the contents of the personal unconscious. For Jung, it must offer the solution to the one-sidedness of the dreamer's ego, leading to better integration/adaptation and a response to the
demands/requirements of his/her life.
Amplification Vs Free Associations
Finally, Jung introduces the amplification method, if necessary, which appeals to materials foreign to the dream such as
myths, symbols, ancestral beliefs, the history of religions.
Freud appeals to the free associations of the dreamer, although he also accepts a symbolism that only refers to sexual matters.
Interestingly, a dream
can be interpreted using both methods: Freud and Jung. The second being somehow the continuation of the first. The result is amazing.
I wrote a special article to illustrate this technique published in our course