This information comes to me from Steven C. Davis who has been invaluable to me in my continuing understanding of the inner workings of the LDS Church.
These two groups are generalizations. You must realize that they represent not a path but a common perspective that sometimes coincides with a path to power. The two groups are basically ecclesiastic prophet led groups of LDS leaders and corporate prophet led groups of LDS leaders.
It appears that the ecclesiastical tendency in church leadership comes from people with mostly a canon-based, rising through the priestly ranks, often with a "royal" approach to leadership. It can be seen as a Joseph Smith inspired and often esoteric pattern.
The other approach to church leadership comes from a Brigham Young inspired model. It is one of a pragmatic and often exoteric organization. Where Joseph Smith hid many secrets about his prophethood, Young administered his secrets of the endowment and plural marriage to all.
This model of outward religous government as opposed to a more ecclesiastical and spiritually shrouded government can be found in the earliest Christianity even to Jesus himself. He was more esoteric and ruled with a mystery shroud. His successors were less esoteric in their approaches.