Howdy-
The western style or full wrap is better suited for steep slopes, due to the fact that production timber fallers in the west cut a lot of timber "on contour" or "parallel to the lay". This means approaching a lot of trees from either side and the ability to flip the saw is a big help. If you're gunning a giant tree and you can hold the saw with the bar facing up, you'll get a better view when making your face cuts.
Western softwoods are worthless below the buttress, since stump wood in the west tends to be twisted, defective, or of irregular grain.
Also- If you've ever used hydraulic tree jacks then you know much of a pain in the ass it is to cut a jack seat with a half wrap handle.