What causes horizontal vs vertical bone loss?

Can't answer. In general with osteoporosis bone loss you lose bone density in both the horizontal struts and the vertical trabeculae. The cause of the bone loss, the resorption canals are in all of the trabecular bones horizontal and vertical. Normal bone turnover does this also but in osteoporosis these resorption canals are increased in number and this leads to increased the bone loss.
Let me explain. A form of bone loss secondary to periodontal disease. This form of bone loss is more generalized than vertical bone loss and is characterized by the loss in height of the four walls surrounding the tooth roots. It may affect only the nearby teeth or may involve the entire dental arch.
Chronic vs. Acute. Horizontal bone loss (hbl) usually associated with chronic condition of periodontitis. Vertical bone loss (vbl) usually associated with acute condition of periodontitis. Hbl sometimes reflects the equilibrium establishment between host factors and bacterial products. Vbl reflects an active lesion in favor of bone and attachment destruction. Vbl can be treated with bone graft, hbl cannot.