I used to wear basketball shoes with air max 360, e.g., CB34 line, Duncan's, and more recently 2010 HyperMax, and would roll my ankle on occasion. But sometimes, when I forgot my basketball shoes, I would wear my Kobe V's (and subsequently Kobe VI's).
I never sprained my ankles when wearing the Kobe V's and started thinking that my ankle sprains were, in part, due to the the higher, air max sole being less rigid/stable than the lower, air zoom sole. I know with LeBron's line Nike supposedly strengthened the outer wall of the air max unit, but I'll never go back and ball in anything air max. LeBrons are strictly comfortable walking/standing shoes.