I don’t think it really matters which one you believe. I personally find it a helpful way of thinking about a person – as soul, spirit and body but I don’t necessarily think that is definitely the way it is.
By thinking about them separately I can understand God giving rebirth to my spirit and communing with me by his spirit. I can understand that my soul has been “crucified with Christ and I no longer live, but Christ lives in me” (Galatians 2:20). I also understand that now, “Since we live by the Spirit, let us keep in step with the Spirit” (Galatians 5:25).
However I think we place too much emphasis on big theological words like trichotomy and dichotomy. Theology is supposed to help us understand more about how God works and not confuse us with words we barely understand. Nor is theology meant to be like the man in this picture who just fills his mind with information. Unless theology helps in practical ways to better understand God then it is really of little value.