each approach has its value. I think the split routine probably works better for a bodybuilder. I think the full body approach works better for strongman and powerlifting--although with powerlifting you can do upper and lower.
I typically think about my workouts more in terms of style of workout rather than body parts. As a strongman competitor, I think it is important to have absolute strength, explosive power, mass, conditioning, endurance, ect. (i.e. the full package).
To help me reach these goals, I try to get in four different types of workouts per week; usually working full body each workout. This is what we are planning for the next few weeks.
Sat - strongman event training (uses a lot of things; not so much absolute strength), plus some cardio
Sun - speed bench, explosive high pulls, rack pulls heavy, lats, abs, calves, cardio
Tues - speed squats w/ bands, front squats, max bench exercise, calves, abs, cardio
Thurs - power snatches, overhead press, stones